Search

We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved - cosmology, astrophysics, nuclear, and particle physics - in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. We then round out the discussion by critically summarizing all known constraints on sterile neutrino Dark Matter arising from astrophysical observations, laboratory experiments, and theoretical considerations. In this context, we provide a balanced discourse on the possibly positive signal from X-ray observations. Another focus of the paper concerns the construction of particle physics models, aiming to explain how sterile neutrinos of keV-scale masses could arise in concrete settings beyond the Standard Model of elementary particle physics. The paper ends with an extensive review of current and future astrophysical and laboratory searches, highlighting new ideas and their experimental challenges, as well as future perspectives for the discovery of sterile neutrinos., Comment: v2: 257 pages, 57 figures, content matches published version [JCAP01(2017)025]; over 100 authors from several different communities

We find the distribution function f(E) for dark matter (DM) halos in galaxies and the corresponding equation of state from the (empirical) DM density profiles derived from observations. We solve for DM in galaxies the analogous of the Eddington equation originally used for the gas of stars in globular clusters. The observed density profiles are a good realistic starting point and the distribution functions derived from them are realistic. We do not make any assumption about the DM nature, the methods developed here apply to any DM kind, though all results are consistent with Warm DM. With these methods we find: (i) Cored density profiles behaving quadratically for small distances rho(r) r -> 0 = rho(0) - K r^2 produce distribution functions which are finite and positive at the halo center while cusped density profiles always produce divergent distribution functions at the center. (ii) Cored density profiles produce approximate thermal Boltzmann distribution functions for r < 3 r_h where r_h is the halo radius. (iii) Analytic expressions for the dispersion velocity and the pressure are derived yielding an ideal DM gas equation of state with local temperature T(r) = m v^2(r)/3. T(r) turns to be constant in the same region where the distribution function is thermal and exhibits the same temperature within the percent. The self-gravitating DM gas can thermalize despite being collisionless because it is an ergodic system. (iv) The DM halo can be consistently considered at local thermal equilibrium with: (a) a constant temperature T(r) = T_0 for r < 3 \; r_h, (b) a space dependent temperature T(r) for 3 r_h < r < R_{virial}, which slowly decreases with r. That is, the DM halo is realistically a collisionless self-gravitating thermal gas for r < R_{virial}. (v) T(r) outside the halo radius nicely follows the decrease of the circular velocity squared., Comment: 24 pages, 8 figures, Discussion on thermalization and ergodicity added

The Thomas-Fermi approach to galaxy structure determines selfconsistently and nonlinearly the gravitational potential of the fermionic WDM particles given their quantum distribution function f(E). Galaxy magnitudes as the halo radius r_h, mass M_h, velocity dispersion and phase space density are obtained. We derive the general equation of state for galaxies (relation between the pressure and the density), and provide an analytic expression. This clearly exhibits two regimes: (i) Large diluted galaxies for M_h > 2.3 10^6 Msun corresponding to temperatures T_0 > 0.017 K, described by the classical self gravitating WDM Boltzman regime and (ii) Compact dwarf galaxies for 1.6 10^6 Msun > M_h>M_{h,min}=30000 (2keV/m)^{16/5} Msun, T_0<0.011 K described by the quantum fermionic WDM regime. The T_0=0 degenerate quantum limit predicts the most compact and smallest galaxy (minimal radius and mass M_{h,min}). All magnitudes in the diluted regime exhibit square root of M_h scaling laws and are universal functions of r/r_h when normalized to their values at the origin or at r_h. We find that universality in galaxies (for M_h > 10^6 Msun) reflects the WDM perfect gas behaviour. These theoretical results contrasted to robust and independent sets of galaxy data remarkably reproduce the observations. For the small galaxies, 10^6>M_h>M_{h,min} corresponding to effective temperatures T_0 < 0.017 K, the equation of state is galaxy dependent and the profiles are no more universal. These non-universal properties in small galaxies account to the quantum physics of the WDM fermions in the compact regime. Our results are independent of any WDM particle physics model, they only follow from the gravitational interaction of the WDM particles and their fermionic quantum nature., Comment: 21 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1309.2290

The third Workshop of the NuMass series ("The Future of Neutrino Mass Measurements: Terrestrial, Astrophysical, and Cosmological Measurements in the Next Decade: NuMass 2013") was held at Dipartimento di Fisica "G. Occhialini, University of Milano-Bicocca in Milano, Italy, on 4-7 February 2013. The goal of this international workshop was to review the status and future of direct and indirect neutrino mass measurements in the laboratory as well as from astrophysical and cosmological observations. This paper collects most of the contributions presented during the Workshop.

The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems: neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies follow from the quantum degenerate regime, while dilute and large galaxies from the classical Boltzmann regime. We find analytic scaling relations for the main galaxy magnitudes as halo radius r_h, mass M_h and phase space density. The observational data for a large variety of galaxies are all well reproduced by these theoretical scaling relations. For the compact dwarfs, our results show small deviations from the scaling due to quantum macroscopic effects. We contrast the theoretical curves for the circular velocities and density profiles with the observational ones. All these results are independent of any WDM particle physics model, they only follow from the gravity interaction of the WDM particles and their fermionic nature. The theory rotation and density curves reproduce very well for r < r_h the observations of 10 different and independent sets of data for galaxy masses from 5x10^9 Msun till 5x10^{11} Msun. Our normalized circular velocity curves turn to be universal functions of r/r_h for all galaxies and reproduce very well the observational curves for r < r_h. Conclusion: the Thomas-Fermi approach correctly describes the galaxy structures (Abridged)., Comment: 14 pages, 8 figures. To be published in MNRAS. arXiv admin note: text overlap with arXiv:1310.6355

Analytic formulas reproducing the warm dark matter (WDM) primordial spectra are obtained for WDM particles decoupling in and out of thermal equilibrium which provide the initial data for WDM non-linear structure formation. We compute and analyze the corresponding WDM overdensities and compare them to the CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2} and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length where the WDM spectrum and overdensity are 1/2 of the respective CDM magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle mass m while the self-similar functions are independent of m. The WDM primordial spectrum sharply decreases around k_{1/2} with respect to the CDM spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The nonlinear regions where WDM structure formation takes place are shown and compared to those in CDM: the WDM non-linear structures start to form later than in CDM, and as a general trend, decreasing the DM particle mass delays the onset of the non-linear regime. The non-linear regime starts earlier for smaller objects than for larger ones; smaller objects can form earlier both in WDM and CDM. We compute and analyze the differential mass function dN/dM for WDM at redshift z in the Press-Schechter approach. The WDM suppression effect of small scale structure increases with the redshift z. Our results for dN/dM are useful to be contrasted with observations, in particular for 4 < z < 12. We perfom all these studies for the most popular WDM particle physics models. Contrasting them to observations should point out the precise value of the WDM particle mass in the keV scale, and help to single out the best WDM particle physics model (Abridged)., Comment: 18 pages, 8 figures. To appear in Phys Rev D

LWDM (Warm Dark Matter) is progressing impressively.The galactic scale crisis and decline of LCDM+baryons are staggering. The 16th Paris Chalonge Colloquium 2012 combined real cosmological/astrophysical data and hard theory predictive approach in the LWDM Standard Model. News and reviews from ACT,WMAP,SPT,QUIET,Planck,Herschel,JWST,UFFO,KATRIN and MARE experiments; astrophysics, particle and nuclear physics WDM searches, galactic observations, related theory and simulations, with the aim of synthesis and clarification. Here highlights by P Biermann, C Burigana, C Conselice, A Cooray, H de Vega, C Giunti & M Laveder, J Kormendi & K Freeman, E Ma, J Mather, L Page, G Smoot, N Sanchez. Summary and conclusions by de Vega, Falvella and Sanchez. Data confirm primordial CMB gaussianity. Effective (Ginsburg-Landau) Inflation theory predicts r about 0.04-0.05, negligeable running of ns, the inflation energy scale (GUT scale) and the set of CMB observables in agreement with the data. WMAP9 and Planck measurements are compatible with one or two Majorana sterile neutrinos in the eV mass scale. Cored (non cusped) DM halos and keV WDM are strongly favored by theory and observations, Wimps are strongly disfavoured. LambdaCDM with baryons do not work at small scales. Inside galaxy cores, quantum WDM effects are important. Quantum WDM calculations (Thomas-Fermi) provide galaxy masses, velocity dispersions and cored profiles and their sizes in agreement with observations. A WDM fermion of about 2 keV naturally reproduces galaxy, large scale and cosmological observations. WDM keV particles deserve dedicated astronomical and laboratory searches, theoretical work and numerical simulations. KATRIN can be adapted to look to keV scale sterile neutrinos. It will be a fantastic discovery to detect dark matter in beta decay. Photos of the Colloquium are included, Comment: 58 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1203.3562, arXiv:1305.7452, arXiv:1009.3494, arXiv:1304.0759

Warm Dark Matter(WDM), considerably clarifies and simplifies galaxies and galaxy formation in agreement with observations. WDM essentially works, naturally reproducing the astronomical observations over all scales, small (galactic) as well as large and cosmological scales.Evidence that CDM, CDM+baryons and proposed tailored cures do not work in galaxies is staggering, The Chalonge Meudon Workshop 2012 approached DM in a fourfold coherent way: astronomical observations (galaxy and cluster properties, haloes, rotation curves, density profiles, surface density), LambdaWDM N-body simulations, WDM theory (Boltzmann-Vlasov evolution, halo mass functions, halo models, improved perturbative approachs), quantum WDM fermions forming the observed cores, WDM particle and nuclear physics (sterile neutrinos) and its experimental search. N Amorisco, P Biermann, S Das, H J de Vega, A Kamada, E Ferri(MARE),I D Karanchetsev, W Liao, M Lovell, M Papastergis, N G Sanchez, P Valageas,C Watson, J Zavala,He Zhang present their Highlights.Inside galaxy cores, N-body classical physics simulations are incorrect for WDM because of important quantum effects at such scales.Quantum WDM calculations (Thomas-Fermi) provide galaxy cores, galaxy masses, velocity dispersions and density profiles in agreement with observations.Baryons (16% of DM) are expected to give a correction to pure WDM results. The summary and conclusions by H. J. de Vega and N. G. Sanchez stress that all evidences point to a DM particle mass around 2 keV. Peter Biermann in his live minutes concludes that a few keV sterile neutrino is the most serious DM candidate. MARE -and hopefully KATRIN- could provide a sterile neutrino signal.There is a formidable WDM work to perform ahead of us, these highlights point research directions worthwhile to pursue.Photos of the Workshop are included (Abridged)., Comment: 61 pages, 19 figures, latex typos corrected

Warm dark matter (WDM) means DM particles with mass m in the keV scale. For large scales, (structures beyond ~ 100 kpc) WDM and CDM yield identical results which agree with observations. For intermediate scales, WDM gives the correct abundance of substructures. Inside galaxy cores, below ~ 100 pc, N-body WDM classical physics simulations are incorrect because at such scales quantum WDM effects are important. WDM quantum calculations (Thomas-Fermi approach) provide galaxy cores, galaxy masses, velocity dispersions and density profiles in agreement with the observations. For a dark matter particle decoupling at thermal equilibrium (thermal relic), all evidences point out to a 2 keV particle. Remarkably enough, sterile neutrinos decouple out of thermal equilibrium with a primordial power spectrum similar to a 2 keV thermal relic when the sterile neutrino mass is about 7 keV. Therefore, WDM can be formed by 7 keV sterile neutrinos. Excitingly enough, Bulbul et al. (2014) announced the detection of a cluster X-ray emission line that could correspond to the decay of a 7.1 keV sterile neutrino and to a neutrino decay mixing angle of \sin^2 2 \theta ~ 7 10^{-11} . This is a further argument in favour of sterile neutrino WDM. Baryons, represent 10 % of DM or less in galaxies and are expected to give a correction to pure WDM results. The detection of the DM particle depends upon the particle physics model. Sterile neutrinos with keV scale mass (the main WDM candidate) can be detected in beta decay for Tritium and Renium and in the electron capture in Holmiun. The sterile neutrino decay into X rays can be detected observing DM dominated galaxies and through the distortion of the black-body CMB spectrum. So far, not a single valid objection arose against WDM., Comment: 18 pages, 7 figures. Based on Lectures by H J de V at NuMass 2013, Milano-Bicocca, Feb 2013; at Cosmic Frontiers, SLAC, March 2013 and by H J de V and N G S at the Chalonge Torino Colloquium 2013, Apr 2013 and The Paris Chalonge Colloquium July 2014. Updated and expanded version

Quantum mechanics is necessary to compute galaxy structures at kpc scales and below. This is so because near the galaxy center, at scales below 10 - 100 pc, warm dark matter (WDM) quantum effects are important: observations show that the interparticle distance is of the order of, or smaller than the de Broglie wavelength for WDM. This explains why all classical (non-quantum) WDM N-body simulations fail to explain galactic cores and their sizes. We describe fermionic WDM galaxies in an analytic semiclassical framework based on the Thomas-Fermi approach, we resolve it numerically and find the main physical galaxy magnitudes: mass, halo radius, phase-space density, velocity dispersion, fully consistent with observations, including compact dwarf galaxies. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed galaxy DM cores and their sizes. [In addition, as is known, WDM simulations produce the right DM structures in agreement with observations for scales > kpc]. We show that compact dwarf galaxies are natural quantum macroscopic objects supported against gravity by the fermionic WDM quantum pressure (quantum degenerate fermions) with a minimal galaxy mass and minimal velocity dispersion. Interestingly enough, the minimal galaxy mass implies a minimal mass m_{min} for the WDM particle. The lightest known dwarf galaxy (Willman I) implies m > m_{min} = 1.91 keV. These results and the observed halo radius and mass of the compact galaxies provide further indication that the WDM particle mass m is approximately around 2 keV., Comment: 15 pages, 2 figures, expanded version to appear in Astroparticle Physics. admin note: substantial text overlap with arXiv:1204.3090

We derive the main physical galaxy properties: mass, halo radius, phase space density and velocity dispersion from a semiclassical gravitational approach in which fermionic WDM is treated quantum mechanically. They turn out to be compatible with observations. Pauli Principle implies for the fermionic DM phase-space density Q(r) = rho(r)/sigma^3(r) the quantum bound Q(r) < K m^4/hbar^3, where m is the DM particle mass, sigma(r) is the DM velocity dispersion and K is a pure number of order one which we estimate. N-body galaxy simulations produce a divergent Q(r) at r = 0 violating this quantum bound. Combining this bound with the behaviour of Q(r) from simulations, the virial and galaxy data on Q implies lower bounds on the halo radius and a minimal distance r_{min} at which classical dynamics for DM fermions breaks down. This quantum bound rules out the presence of galaxy cusps for fermionic WDM, in agreement with astronomical observations, which show that the DM halos are cored. We show that compact dwarf galaxies are quantum objects supported against gravity by the fermionic WDM quantum pressure. Quantum mechanical calculations become necessary to compute galaxy structures at kpc scales and below. Classical N-body simulations are not valid at scales below r_{min}. We apply the Thomas-Fermi semiclassical approach to fermionic WDM galaxies and find the physical magnitudes: mass, halo radius, phase-space density, velocity dispersion, consistent with observations especially for compact dwarf galaxies. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the sizes of the observed cores. The lightest known galaxy Willman I implies a lower bound for the WDM particle mass m > 0.96 keV. These results and the observed galaxies with halo radius > 30 pc and halo mass > 4 10^5 M_sun provide further indication that the WDM particle mass m is in the range 1-2 keV., Comment: 25 pages, 2 figures. To appear in New Astronomy

The Chalonge 15th Paris Cosmology Colloquium 2011 was held on 20-22 July in the historic Paris Observatory's Perrault building, in the Chalonge School spirit combining real cosmological/astrophysical data and hard theory predictive approach connected to them in the Warm Dark Matter Standard Model of the Universe: News and reviews from Herschel, QUIET, Atacama Cosmology Telescope (ACT), South Pole Telescole (SPT), Planck, PIXIE, the JWST, UFFO, KATRIN and MARE experiments; astrophysics, particle and nuclear physics warm dark matter (DM) searches and galactic observations, related theory and simulations, with the aim of synthesis, progress and clarification. Philippe Andre, Peter Biermann, Pasquale Blasi, Daniel Boyanovsky, Carlo Burigana, Hector de Vega, Joanna Dunkley, Gerry Gilmore, Alexander Kashlinsky, Alan Kogut, Anthony Lasenby, John Mather, Norma Sanchez, Alexei Smirnov, Sylvaine Turck-Chieze present here their highlights of the Colloquium. Ayuki Kamada and Sinziana Paduroiu present here their poster highlights. LambdaWDM (Warm Dark Matter) is progressing impressively over LambdaCDM whose galactic scale crisis and decline are staggering. The International School Daniel Chalonge issued an statement of strong support to the James Webb Space Telescope (JSWT). The Daniel Chalonge Medal 2011 was awarded to John C. Mather, Science PI of the JWST. Summary and conclusions are presented by H. J. de Vega, M. C. Falvella and N. G. Sanchez. Overall, LambdaWDM and keV scale DM particles deserve dedicated astronomical and laboratory experimental searches, theoretical work and simulations. KATRIN experiment in the future could perhaps adapt its set-up to look to keV scale sterile neutrinos. It will be a a fantastic discovery to detect dark matter in a beta decay. Photos of the Colloquium are included. (Abridged), Comment: 65 pages, 21 figures

We study the complete cosmological evolution of dark matter (DM) density fluctuations for DM particles that decoupled being ultrarelativistic during the radiation dominated era which is the case of keV scale warm DM (WDM). The new framework presented here can be applied to other types of DM and in particular we extend it to cold DM (CDM). The collisionless and linearized Boltzmann-Vlasov equations (B-V) for WDM and neutrinos in the presence of photons and coupled to the linearized Einstein equations are studied in detail in the presence of anisotropic stress with the Newtonian potential generically different from the spatial curvature perturbations. We recast this full system of B-V equations for DM and neutrinos into a system of coupled Volterra integral equations. These Volterra-type equations are valid both in the radiation dominated (RD) and matter dominated (MD) eras during which the WDM particles are ultrarelativistic and then nonrelativistic. This generalizes the so-called Gilbert integral equation only valid for nonrelativistic particles in the MD era. We succeed to reduce the system of four Volterra integral equations for the density and anisotropic stress fluctuations of DM and neutrinos into a system of only two coupled Volterra equations. The kernels and inhomogeneities in these equations are explicitly given functions. Combining the Boltzmann-Vlasov equations and the linearized Einstein equations constrain the initial conditions on the distribution functions and gravitational potentials. In the absence of neutrinos the anisotropic stress vanishes and the Volterra-type equations reduce to a single integral equation. These Volterra integral equations provide a useful and precise framework to compute the primordial WDM fluctuations over a wide range of scales including small scales up to k ~ 1/5 kpc., Comment: 26 pages, 1 figure. To appear in Phys Rev D

We solve the cosmological evolution of warm dark matter (WDM) density fluctuations with the Volterra integral equations of paper I. In the absence of neutrinos, the anisotropic stress vanishes and the Volterra equations reduce to a single integral equation. We solve numerically this equation both for DM fermions decoupling at equilibrium and DM sterile neutrinos decoupling out of equilibrium. We give the exact analytic solution for the density fluctuations and gravitational potential at zero wavenumber. We compute the density contrast as a function of the scale factor a for a wide range of wavenumbers k. At fixed a, the density contrast grows with k for k < k_c while it decreases for k > k_c, (k_c ~ 1.6/Mpc). The density contrast depends on k and a mainly through the product k a exhibiting a self-similar behavior. Our numerical density contrast for small k gently approaches our analytic solution for k = 0. For fixed k < 1/(60 kpc), the density contrast generically grows with a while for k > 1/(60 kpc) it exhibits oscillations since the RD era which become stronger as k grows. We compute the transfer function of the density contrast for thermal fermions and for sterile neutrinos in: a) the Dodelson-Widrow (DW) model and b) in a model with sterile neutrinos produced by a scalar particle decay. The transfer function grows with k for small k and then decreases after reaching a maximum at k = k_c reflecting the time evolution of the density contrast. The integral kernels in the Volterra equations are nonlocal in time and their falloff determine the memory of the past evolution since decoupling. This falloff is faster when DM decouples at equilibrium than when it decouples out of equilibrium. Although neutrinos and photons can be neglected in the MD era, they contribute in the MD era through their memory from the RD era., Comment: 27 pages, 6 figures. To appear in Phys Rev D

Sterile neutrinos with mass in the range of one to a few keV are important as extensions of the Standard Model of particle physics and are serious dark matter (DM) candidates. This DM mass scale (warm DM) is in agreement with both cosmological and galactic observations. We study the role of a keV sterile neutrino through its mixing with a light active neutrino in Rhenium 187 and Tritium beta decays. We pinpoint the energy spectrum of the beta particle, 0 < T_e < (Q_{beta} - m_s), as the region where a sterile neutrino could be detected and where its mass m_s could be measured. This energy region is at least 1 keV away rom the region suitable to measure the mass of the light active neutrino, located near the endpoint Q_{beta} . The emission of a keV sterile neutrino in a beta decay could show up as a small kink in the spectrum of the emitted beta particle. With this in view, we perform a careful calculation of the Rhenium and Tritium beta spectra and estimate the size of this perturbation by means of the dimensionless ratio R of the sterile neutrino to the active neutrino contributions. We comment on the possibility of searching for sterile neutrino signatures in two experiments which are currently running at present, MARE and KATRIN, focused on the Rhenium 187 and Tritium beta decays respectively., Comment: 16 pages, 10 figures. Version to appear in Nucl. Phys. B. Results and conclusions unchanged

Warm Dark Matter (WDM) research is progressing fast, the subject is new and WDM essentially works, naturally reproducing the astronomical observations over all scales: small (galactic) and large (cosmological) scales (LambdaWDM). Evidence that Cold Dark Matter (LambdaCDM) and its proposed tailored cures do not work at small scales is staggering. Fedor Bezrukov, Pier-Stefano Corasaniti, Hector J. de Vega, Stefano Ettori, Frederic Hessmann, Ayuki Kamada, Marco Lombardi, Alexander Merle, Christian Moni Bidin, Angelo Nucciotti on behalf of the MARE collaboration, Sinziana Paduroiu, Henri Plana, Norma Sanchez, Patrick Valageas, Shun Zhou present here their highlights of the Workshop. LambdaWDM simulations with keV particles remarkably reproduce the observations, small and large structures and velocity functions. Cored DM halos and WDM are clearly determined from theory and astronomical observations, they naturally produce the observed structures at all scales. keV sterile neutrinos are the leading candidates, they naturally appear extensions of the standard model of particle physics. Astrophysical constraints including Lyman alpha bounds put its mass in the range 1< m <13 keV. Predictions for EUCLID and PLANCK have been presented. MARE and an adapted KATRIN experiment could detect a keV sterile neutrino. It will be a fantastic discovery to detect dark matter in a beta decay. A formidable WDM work to perform is ahead of us, these highlights point out some relevant research directions to put the effort. Photos of the Workshop are included (Abridged)., Comment: 48 pages, 24 figures

The Chalonge 14th Paris Cosmology Colloquium was held on 22-24 July 2010 in Paris Observatory on the Standard Model of the Universe: News from WMAP7, BICEP, QUAD, SPT, AMI, ACT, Planck, QUIJOTE and Herschel; dark matter (DM) searches and galactic observations; related theory and simulations. %aiming synthesis, progress and clarification. P Biermann, D Boyanovsky, A Cooray, C Destri, H de Vega, G Gilmore, S Gottlober, E Komatsu, S McGaugh, A Lasenby, R Rebolo, P Salucci, N Sanchez and A Tikhonov present here their highlights of the Colloquium. Inflection points emerged: LambdaWDM (Warm DM) emerges impressively over LambdaCDM whose galactic scale problems are ever-increasing. Summary and conclusions by H. J. de Vega, M. C. Falvella and N. G. Sanchez stress among other points: (i) Primordial CMB gaussianity is confirmed. Inflation effective theory predicts a tensor to scalar ratio 0.05-0.04 at reach/border line of next CMB observations, early fast-roll inflation provides lowest multipoles depression. SZ amplitudes are smaller than expected: CMB and X-ray data agree but intracluster models need revision and relaxed/non-relaxed clusters distinction. (ii) cosmic ray positron excess is explained naturally by astrophysical processes, annihilating/decaying dark matter needs growing tailoring. (iii) Cored (non cusped) DM halos and warm (keV scale mass) DM are increasingly favored from theory and observations, naturally producing observed small scale structures, wimps turn strongly disfavoured. LambdaWDM 1 keV simulations well reproduce observations. Evidence that LambdaCDM does not work at small scales is staggering. P Biermann presents his live minutes of the Colloquium and concludes that a keV sterile neutrino is the most interesting DM candidate. Photos of the Colloquium are included., Comment: 58 pages, 20 figures. Three contributions added: G. Gilmore, S. Gottlober and E. Komatsu

The 13th Chalonge Paris Cosmology Colloquium was held at the historic Perrault building of Observatoire de Paris on 23-25 July 2009. The Colloquium was held in the spirit of the Chalonge School, putting together real cosmological and astrophysical data and hard theory predictive approach in the framework of the Standard Model of the Universe. Peter Biermann, James Bullock, Claudio Destri, Hector de Vega, Massimo Giovannini, Sasha Kashlinsky, Eiichiro Komatsu, Anthony Lasenby and Norma G. Sanchez present here their highlights of the Colloquium. The summary and conclusions by H. J. de Vega, M. C. Falvella and N. G. Sanchez stress among other points: (i) the primordial CMB fluctuations are almost gaussian, large primordial non-gaussianity and large running index are strongly disfavored. The primordial graviton ratio r is predicted in the effective theory of inflation to be between 0.021 and 0.053, at reach of the next CMB observations. (ii) Dark energy observations are consistent with the cosmological constant. (iii) The cosmic ray positron excess recently observed is explained by natural astrophysical processes. (iv) The heavy dark matter particle candidates ( > 1 GeV, wimps) became strongly disfavored, while cored (non cusped) dark matter halos and light (keV scale mass) dark matter are being increasingly favored from theory and astrophysical observations. The Daniel Chalonge Medal 2009 was awarded to Peter Biermann during the Colloquium. Photos of the Colloquium are included., Comment: 22 pages, 3 pictures. Problem with the poster fixed

The CIAS Chalonge Workshop `Dark Matter in the Universe and Universal Properties of Galaxies: Theory and Observations', was held at the Meudon Ch^ateau of Observatoire de Paris on 8-11 June 2010. The Workshop approached DM in a fourfold way: astronomical observations of DM structures (galaxy properties, halos, rotation curves and density profiles), DM numerical simulations (with and without baryons), theoretical astrophysics and cosmology (kinetic theory, Boltzmann-Vlasov evolution), astroparticle physics. Peter Biermann, Alfonso Cavaliere, Hector J. de Vega, Gianfranco Gentile, Chandra Jog, Andrea Lapi, Paolo Salucci, Norma G. Sanchez, Pasquale Serpico, Rainer Stiele, Janine van Eymeren and Markus Weber present here their highlights of the Workshop. The summary and conclusions by H. J. de Vega and N. G. Sanchez stress among other points the growing evidence that DM particles have a mass in the keV scale and that those keV scale particles naturally produce the small scale structures observed in galaxies. Wimps (DM particles heavier than 1 GeV) are strongly disfavoured combining theory with galaxy astronomical observations. Peter Biermann presents his live minutes of the Workshop and concludes that a right-handed sterile neutrino of mass of a few keV is the most interesting DM candidate. Photos of the Workshop are included., Comment: 41 pages, 10 figures, 3 photos. Problem in group photo fixed

We present here the effective theory of inflation `a la Ginsburg-Landau in which the inflaton potential is a polynomial. The slow-roll expansion becomes a systematic 1/N expansion where N ~ 60. The spectral index and the ratio of tensor/scalar fluctuations are n_s - 1 = O(1/N), r = O(1/N) while the running turns to be d n_s/d \ln k = O(1/N^2) and can be neglected. The energy scale of inflation M ~ 0.7 10^{16} GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov Chains (MCMC) analysis of the available CMB+LSS data showed: (a) the spontaneous breaking of the phi -> - phi symmetry of the inflaton potential. (b) a lower bound for r: r > 0.023 (95% CL) and r > 0.046 (68% CL). (c) The preferred inflation potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: n_s = 0.964, r = 0.051. This value for r is within reach of forthcoming CMB observations. We investigate the DM properties using cosmological theory and the galaxy observations. Our DM analysis is independent of the particle physics model for DM and it is based on the DM phase-space density rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM particle mass m and for the number of ultrarelativistic degrees of freedom g_d (hence the temperature) at decoupling. We find that m turns to be at the keV scale. The keV scale DM is non-relativistic during structure formation, reproduces the small and large scale structure but it cannot be responsible of the e^+ and pbar excess in cosmic rays which can be explained by astrophysical mechanisms (Abridged)., Comment: 28 pages; to be published in the Lev Lipatov Festschrift on the occasion of Lev's 70th birthday, `Subtleties in Quantum Field Theories', D. Diakonov, Editor, Gatchina, Russia, 2010

We combine observed properties of galaxies as the core density and radius with the theoretical linear evolution of density fluctuations computed from first principles since the end of inflation till today. The halo radius r_0 is computed in terms of cosmological parameters. The theoretical density profiles rho(r)/rho(0) have an universal shape as a function of r/r_0 which reproduces the observations. We show that the linear approximation to the Boltzmann-Vlasov equation is valid for very large galaxies and correctly provides universal quantities which are common to all galaxies, as the surface density and density profile. By matching the theoretically computed surface density to its observed value we obtain (i) the decreasing of the phase-space density during the MD era (ii) the mass of the dark matter particle which turns to be between 1 and 2 keV and the decoupling temperature T_d which turns to be above 100 GeV (iii) the core vs. cusp discrimination: keV dark matter particles produce cored density profiles while wimps (m \sim 100 GeV, T_d \sim 5 GeV) produce cusped profiles at scales about 0.003 pc. These results are independent of the particle model and vary very little with the statistics of the dark matter particle. Non-universal galaxy quantities (which need to include non-linear effects as mergers and baryons) are reproduced in the linear approximation up to a factor of order one for the halo radius r_0, galaxy mass M_{gal}, halo central density rho_{0} and velocity dispersion sqrt{{\bar {v^2}}_{halo}} in the limiting case of large galaxies (both r_0 and M_{gal} large). This shows the power of the linear approximation scheme: although it cannot capture the whole content of the structure formation, it correctly provides universal quantities which as well as the main non-universal galaxy properties., Comment: 17 pages, 15 figures, improved and expanded version to appear in New Astronomy

The Planck satellite is right now measuring with unprecedented accuracy the primary Background CMB anisotropies. The Standard Model of the Universe (including inflation) provides the context to analyze the CMB and other data. The Planck performance for r, the tensor to scalar ratio related to primordial B mode polarization, will depend on the quality of the data analysis. The Ginsburg Landau approach to inflation allows to take high benefit of the CMB data. The fourth degree double well inflaton potential gives an excellent fit to the current CMB+LSS data. We evaluate the Planck precision to the recovery of cosmological parameters within a reasonable toy model for residuals of systematic effects of instrumental and astrophysical origin based on publicly available information.We use and test two relevant models: the LambdaCDMr model, i.e. the standard LambdaCDM model augmented by r, and the LambdaCDMrT model, where the scalar spectral index, n_s, and r are related through the theoretical `banana-shaped' curve r = r(n_s) coming from the double-well inflaton potential. In the latter case, r = r(n_s) is imposed as a hard constraint in the MCMC data analysis. We take into account the white noise sensitivity of Planck in the 70, 100 and 143 GHz channels as well as the residuals from systematics errors and foregrounds. Foreground residuals turn to affect only the cosmological parameters sensitive to the B modes. The best value for r in the presence of residuals turns to be about r simeq 0.04 for both the LambdaCDMr and the LambdaCDMrT models. We compute the B mode detection probability by the most sensitive HFI-143 channel. At the level of foreground residual equal to 30% of our toy model only a 68% CL detection of r is very likely. For a 95% CL detection the level of foreground residual should be reduced to 10% or lower of the adopted toy model (ABRIDGED)., Comment: 26 pages, 11 figures. Expanded version to be published in ApJ

We study the entire coupled evolution of the inflaton and the scale factor for general initial conditions at a given initial time. The generic early universe evolution has three stages: decelerated fast-roll followed by inflationary fast roll and then inflationary slow-roll. This evolution is valid for all regular inflaton potentials. In addition, we find a special (extreme) slow-roll solution starting at t = -infty in which the fast-roll stages are absent. At some time t = t_*, the generic evolution backwards in time reaches a mathematical singu- larity where a(t) vanishes and Hubble becomes singular. We find the general behaviour near the singularity. The classical inflaton description is valid for t-t_* > 10 t_{Planck} well before the beginning of inflation, quantum loop effects are negligible there. The singularity is never reached in the validity region of the classical treatment and therefore it is not a real physical phenomenon here. The whole evolution of the fluctuations is computed. The Bunch-Davies initial conditions (BDic) are generalized for the present case. The power spectrum gets dynamically modified by the effect of the fast-roll eras and the BDic choice at a finite time through the transfer function D(k) of initial conditions. D(0) = 0. D(k) presents a first peak for k ~ 2/eta_0 (eta_0 being the conformal initial time), then oscillates with decreasing amplitude and vanishes asymptotically for k -> infty. The transfer function D(k) affects the low CMB multipoles C_l: the change Delta C_l/C_l for l=1-5 is computed as a function of the starting instant of the fluctuations t_0. CMB quadrupole observations give large suppressions which are well reproduced here(Abridged), Comment: 31 pages, 10 figures. Version to appear in PRD

Cumulative observational evidence confirm that the surface gravity of dark matter (DM) halo mu_{0 D} = r_0 rho_0 where r_0 and rho_0 are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value mu_{0 D} = 140 M_{sun}/pc^2 = (18.6 Mev)^3 is approximately the same (up to a factor of two) in all these systems. First, we present the physical consequences of the independence of mu_{0 D} on r_0: the energy scales as the volume sim r_0^3 while the mass and the entropy scale as the surface ~ r_0^2 and the surface times log r_0, respectively. Namely, the entropy scales similarly to the black-hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and the evolution of primordial density fluctuations since the end of inflation till today using the linearized Boltzmann-Vlasov equation. The density profile rho_{lin}(r) obtained in this way decreases as r^{-1-n_s/2} for intermediate scales where n_s = 0.964 is the primordial spectral index. This scaling is in remarkable agreement with the empirical behaviour found observationally and in N-body simulations: r^{-1.6\pm 0.4}. The observed value of mu_{0 D} indicates that the DM particle mass m is in the keV scale. The theoretically derived density profiles rho_{lin}(r) turn to be cored for m in the keV scale and they look as cusped for m in the GeV scale or beyond. We consider both fermions and bosons as DM particles decoupling either ultrarelativistically or non-relativistically. Our results do not use any particle physics model and vary slightly with the statistics of the DM particle., Comment: 12 pages, 2 figures. Expanded and improved version to appear in Int J Mod Phys A

The MCMC analysis of the CMB+LSS data in the context of the Ginsburg-Landau approach to inflation indicated that the fourth degree double--well inflaton potential best fits the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r = 0.05, within reach of the forthcoming CMB observations. We systematically analyze here the effects of arbitrary higher order terms in the inflaton potential on the CMB observables: spectral index ns and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns to belong to the Ginsburg-Landau class too. The theoretical values in the (ns,r) plane for all double well inflaton potentials in the Ginsburg-Landau approach (including the potential generated by fermions) turn to be inside a universal banana-shaped region B. The upper border of the banana-shaped region B is given by the fourth order double--well potential and provides an upper bound for the ratio r.The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index ns = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations., Comment: 24 pages, 10 figures. Presentation improved. To appear in Annals of Physics

We present a model independent analysis of dark matter (DM) both decoupling ultra relativistic (UR) and non-relativistic (NR) based in the phase-space density D = rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM particle mass m and for the number of ultra relativistic degrees of freedom g_d at decoupling. We find that for DM particles decoupling UR both at local thermal equilibrium (LTE) and out of LTE, m turns to be at the keV scale. For example, for DM Majorana fermions decoupling at LTE the mass results m ~ 0.85 keV. For DM particles decoupling NR, sqrt{m T_d} results in the keV scale (T_d is the decoupling temperature) and the m value is consistent with the keV scale. In all cases, DM turns to be cold DM (CDM). Also, lower and upper bounds on the DM annihilation cross-section for NR decoupling are derived. We evaluate the free-streaming (Jeans') length and Jeans' mass: they result independent of the type of DM except for the DM self-gravity dynamics. The free-streaming length today results in the kpc range. These results are based on our theoretical analysis, astronomical observations of dwarf spheroidal satellite galaxies in the Milky Way and N-body numerical simulations. We analyze and discuss the results on D from analytic approximate formulas both for linear fluctuations and the (non-linear) spherical model and from N-body simulations results. We obtain in this way upper bounds for the DM particle mass which all result below the 100 keV range., Comment: 11 pages, 2 figures. Expanded version to be published in Monthly Notices of the Royal Astronomical Society

Inflation is part of the Standard Model of the Universe supported by CMB and large scale structure LSS datasets. This review presents new developments of inflation in three main chapters. (I): The effective theory of inflation a la Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal form making explicit the inflation energy scale M, the Planck mass and the inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings are naturally small as powers of (M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV is completely determined by the scalar adiabatic fluctuations amplitude. (II): A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including WMAP5) with our analytic theoretical results yields: a lower bound for r (new inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation potential is a double well, even function of the field yielding as most probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of forthcoming CMB observations. Slow-roll inflation is generically preceded by a short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE modes well reproducing the quadrupole suppression and fixes the total number of efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates the effective theory of inflation. We show how powerful is the GL theory of inflation in predicting observables., Comment: Review article, 134 pages, 41 figures. Int. J. Mod. Phys. A24, 3669-3864 (2009). A few last improvements

Quantum fast-roll initial conditions for the inflaton which are different from the classical fast-roll conditions and from the quantum slow-roll conditions can lead to inflation that last long enough. These quantum fast-roll initial conditions for the inflaton allow for kinetic energies of the same order of the potential energies and nonperturbative inflaton modes with nonzero wavenumbers. Their evolution starts with a transitory epoch where the redshift due to the expansion succeeds to assemble the quantum excited modes of the inflaton in a homogeneous (zero mode) condensate, and the large value of the Hubble parameter succeeds to overdamp the fast-roll of the redshifted inflaton modes. After this transitory stage the effective classical slow-roll epoch is reached. Most of the efolds are produced during the slow-roll epoch and we recover the classical slow-roll results for the scalar and tensor metric perturbations plus corrections. These corrections are important, both for scalar and for tensor perturbations, if scales which are horizon-size today exited the horizon by the end of the transitory stage and as a consequence the lower CMB multipoles get suppressed (fast-roll) or enhanced (precondensate). These two types of corrections can compete and combine in a scale dependent manner. They arise as natural consequences of the quantum nonperturbative inflaton dynamics, and provide a consistent and contrastable model for the origin of the suppression of the quadrupole and for other departures of the low CMB multipoles from the slow-roll inflation-LambdaCMB model which are to be contrasted to the TE and EE multipoles and to the forthcoming and future CMB data., Comment: LaTeX, 14 pages, 3 figures

The transfer function $T(k)$ of dark matter (DM) perturbations during matter domination is obtained by solving the collisionless Boltzmann-Vlasov equation. We find an \emph{exact} expression for $T(k)$ for \emph{arbitrary} distribution functions of decoupled particles and initial conditions}. We find a remarkably accurate and simple approximation valid on all scales of cosmological relevance for structure formation in the linear regime. The natural scale of suppression is the free streaming wavevector at matter-radiation equality, $ k_{fs}(t_{eq}) = [{4\pi\rho_{0M}}/{[< \vec{V}^2> (1+z_{eq})]} ]^\frac12 $. An important ingredient is a non-local kernel determined by the distribution functions of the decoupled particles which describes the \emph{memory of the initial conditions and gravitational clustering} and yields a correction to the fluid description. Distribution functions that favor the small momentum region lead to an \emph{enhancement of power at small scales} $ k > k_{fs}(t_{eq}) $. For DM thermal relics that decoupled while ultrarelativistic we find $ k_{fs}(t_{eq}) \simeq 0.003 (g_d/2)^\frac13 (m/\mathrm{keV}) [\mathrm{kpc}]^{-1} $, where $ g_d $ is the number of degrees of freedom at decoupling. For WIMPS we obtain $ k_{fs}(t_{eq}) = 5.88 (g_d/2)^\frac13 (m/100 \mathrm{GeV})^\frac12 (T_d/10 \mathrm{MeV})^\frac12 [\mathrm{pc}]^{-1} $. For $k\ll k_{fs}(t_{eq})$, $T(k) \sim 1-\mathrm{C}[k/k_{fs}(t_{eq})]^2 $ where $C =\mathrm{O}(1)$ for all cases considered and simple and accurate fits for \emph{small} scales., Comment: 33 pages, 10 figures. Version to appear in PRD

Generically,the classical evolution of the inflaton has a brief fast roll stage that precedes the slow roll regime. The fast roll stage leads to a purely attractive potential for the curvature and tensor perturbations (this potential is purely repulsive in slowroll). This attractive potential depresses the CMB quadrupole moment for the curvature and B-mode spectra. A single new cosmological parameter emerges: the comoving wavenumber k_1 characteristic scale of this attractive potential.k_1 happens to exit the horizon precisely at the transition from fast to slowroll.The fastroll stage dynamically modifies the initial power spectrum by a transfer function D(k). We compute D(k) by solving the inflaton evolution equations. D(k) suppresses the primordial power for k < k_1 and enjoys the scaling property D(k) = Psi(k/k_1) where Psi(x) is an universal function. We perform a MCMC analysis of the WMAP/SDSS data including the fast-roll stage and find k_1 = 0.266/Gpc. The quadrupole mode k_Q = 0.242/Gpc exits the horizon 1/10 of an efold before k_1. We compare the fastroll fit with a fit with a sharp lower cutoff on the primordial power. Fastroll provides a slightly better fit than a sharp cutoff for the TT,TE and EE modes.Moreover, our fits provide non-zero lower bounds for r, while for the other cosmological parameters we essentially get those of the LCDM model. The fact that k_Q exits the horizon before the slowroll stage implies an upper bound in the total number of efolds N_{tot} during inflation.Combining this with estimates during the radiation dominated era we obtain N_{tot} ~ 66, with the bounds 62 < N_{tot} < 82.We repeated the analysis with the WMAP-5/ACBAR-2007/SDSS data confirming the overall picture., Comment: 23 pages, 11 figures. Expanded and improved version to appear in Phys Rev D

Mass bounds on dark matter (DM) candidates are obtained for particles decoupling in or out of equilibrium with {\bf arbitrary} isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase space density $ \mathcal D $ is introduced. Combining its value with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps), the DM density today and $N$-body simulations, yields upper and lower bounds on the mass, primordial phase space densities and velocity dispersion of the DM candidates. The mass of the DM particles is bound in the few keV range. If chemical freeze out occurs before thermal decoupling, light bosonic particles can Bose-condense. Such Bose-Einstein {\it condensate} is studied as a dark matter candidate. Depending on the relation between the critical($T_c$)and decoupling($T_d$)temperatures, a BEC light relic could act as CDM but the decoupling scale must be {\it higher} than the electroweak scale. The condensate tightens the upper bound on the particle's mass. Non-equilibrium scenarios that describe particle production and partial thermalization, sterile neutrinos produced out of equilibrium and other DM models are analyzed in detail obtaining bounds on their mass, primordial phase space density and velocity dispersion. Light thermal relics with $ m \sim \mathrm{few} \mathrm{keV}$ and sterile neutrinos lead to a primordial phase space density compatible with {\bf cored} dShps and disfavor cusped satellites. Light Bose condensed DM candidates yield phase space densities consistent with {\bf cores} and if $ T_c\gg T_d $ also with cusps. Phase space density bounds from N-body simulations suggest a potential tension for WIMPS with $ m \sim 100 \mathrm{GeV},T_d \sim 10 \mathrm{MeV} $., Comment: 27 pages 8 figures. Version to appear in Phys. Rev. D

We perform a MCMC (Monte Carlo Markov Chains) analysis of the available CMB and LSS data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the GinsburgLandau spirit with fourth degree trinomial potentials in the inflaton field phi.We derive explicit formu- lae and study in detail the spectral index ns of the adiabatic fluctuations the ratio r of tensor to scalar fluctuations and the running index dn_s/dln k. We use these analytic formulas as hard constraints on n_s and r in the MCMC analysis.Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follow: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the phi -> -phi symmetry of the inflaton potentials both for new and for chaotic inflation.(ii)Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data.(iii)Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space.(iv) The chaotic symmetric trinomial potential is almost certainly ruled out(at 95% CL).In tri- nomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which ressembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data.(vi) We find a lower bound for r within trinomial new inflation potentials r > 0.016 (95% CL) and r > 0.049 (68% CL). (vii) The preferred new inflation trinomial potential is a double well, even function of the field yielding as most probable values: n_s ~ 0.958, r ~ 0.055. Such r could be observed soon., Comment: 26 pages, 9 figures. Expanded and improved version to appear in Phys. Rev. D

The CMB power spectra are studied for different families of single field new and chaotic inflation models in the effective field theory approach to inflation. We implement a systematic expansion in 1/N_e where N_e ~ 50 is the number of e-folds before the end of inflation. We study the dependence of the observables (n_s, r and dn_s/d\ln k) on the degree of the potential (2 n) and confront them to the WMAP3 and large scale structure data: this shows in general that fourth degree potentials (n=2) provide the best fit to the data; the window of consistency with the WMAP3 and LSS data narrows for growing n. New inflation models yield a good fit to the r and n_s data in a wide range of field and parameter space. Small field inflation yields r<0.16 while large field inflation yields r>0.16 (for N_e=50). All members of the new inflation family predict a small but negative running -4(n+1)10^{-4}< dn_s/d\ln k <-2 10^{-4}. A reconstruction program is carried out suggesting quite generallythat for n_s consistent with the WMAP3 and LSS data and r<0.1 the symmetry breaking scale for new inflation is |\phi_0| ~ 10 M_{Pl} while the field scale at Hubble crossing is |\phi_{50}| ~ M_{Pl}.The family of chaotic models feature r>0.16 (for N_e=50) and only a restricted subset of chaotic models are consistent with the combined WMAP3 bounds on r, n_s,dn_s/d\ln k with a narrow window in field amplitude around |\phi_{50}| ~ 15 M_{Pl}.A measurement of r<0.16 (for N_e =50) will distinctly rule out a large class of chaotic scenarios and will favor new inflationary models. As a general consequence, new inflation emerges more favoured than chaotic inflation., Comment: 19 pages, 18 figures. Minor additions. Matches version published in Phys. Rev. D

We investigate the issue of initial conditions of curvature and tensor perturba- tions at the beginning of slow roll inflation and their effect on the power spectra. Renormalizability and small back reaction constrain the high k behavior of the Bogoliubov coefficients that define these initial conditions.We introduce a transfer function D(k) which encodes the effect of generic initial conditions on the power spectra. The constraint from renormalizability and small back reaction entails that D(k) < mu^2/k^2 for large k, implying that observable effects from initial conditions are more prominent in the low multipoles. This behavior affects the CMB quadrupole by the observed amount \~10-20% when mu is of the order of the energy scale of inflation. The effects on high l-multipoles are suppressed by a factor ~1/l^2 due to the fall off of D(k) for large wavevectors k. We show that the determination of generic initial conditions for the fluc- tuations is equivalent to the scattering problem by a potential V(eta) localized just prior to the slow roll stage. Such potential leads to a transfer function D(k) which automatically obeys the renormalizability and small backreaction constraints. We find that an attractive potential V(eta) yields a suppression of the lower CMB multipoles.Both for curvature and tensor modes, the quadrupole suppression depends only on the energy scale of V(eta) and on the time interval where V(eta) is nonzero. A suppression of the quadrupole for curvature pertur- bations consistent with the data is obtained when the scale of the potential is of the order of k^2_Q where k_Q is the wavevector whose physical wavelength is the Hubble radius today., Comment: Some comments and references added

Within the effective field theory of inflation, an initialization of the classical dynamics of the inflaton with approximate equipartition between the kinetic and potential energy of the inflaton leads to a brief fast roll stage that precedes the slow roll regime. The fast roll stage leads to an attractive potential in the wave equations for the mode functions of curvature and tensor perturbations. The evolution of the inflationary perturbations is equivalent to the scattering by this potential and a useful dictionary between the scattering data and observables is established.Implementing methods from scattering theory we prove that this attractive potential leads to a suppression of the quadrupole moment for CMB and B-mode angular power spectra. The scale of the potential is determined by the Hubble parameter during slow roll. Within the effective field theory of inflation at the grand unification (GUT) energy scale we find that if inflation lasts a total number of efolds N_{tot} ~ 59, there is a 10-20% suppression of the CMB quadrupole and about 2-4% suppression of the tensor quadrupole. The suppression of higher multipoles is smaller, falling off as 1/l^2. The suppression is much smaller for N_{tot} > 59, therefore if the observable suppression originates in the fast roll stage, there is the upper bound N_{tot} ~ 59., Comment: Some comments and references added

The self-gravitating gas in thermal equilibrium is studied using a Newtonian potential regularized at short distances. This short distance cutoff permits us to obtain a complete description of the gas including its collapsed phase. We give a field theory description of the N-body regularized self-gravitating gas in the canonical ensemble.The corresponding functional integral is dominated in the N -> infty limit by saddle points which provide a mean field description. The well-known dilute solutions (isothermal spheres) are recovered. We find new solutions which are regular in the regularized theory but become singular in the zero cutoff limit. They describe collapsed configurations where the particles are densely concentrated in a region of the size of the cutoff. These collapsed solutions provide the absolute minimum of the free energy. We find further new solutions which interpolate between the collapsed and the dilute configurations and describe tunneling processes where the gas collapses. The transition proba- bility for such collapse processes turns out to be extremely small for large N. That is, the dilute solutions are in practice stable in the regime where they are locally stable., Comment: 17 pages, 7 color figures. Some comments and references added. To appear in Nucl. Phys. B

We study the single field slow-roll inflation models that better fit the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study them as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The compute the spectral index n_s of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index d n_s/dln k, derive explicit formulae and provide relevant plots. In new inflation, and for the three years WMAP central value n_s = 0.95, we predict 0.031. Hybrid inflation for mu_0^2>Lambda_0 M_{Pl}^2/192 can fullfill all the present CMB+LSS data. Even if chaotic inflation predicts n_s values compatible with the data, chaotic inflation is disfavoured since it predicts a too high value for the ratio r=0.27. The model which best fits the current data and which best prepares the way to the expected data r < 0.1, is the trinomial potential with negative mass term: new inflation., Comment: Some comments and a few new results added

The evolution of the Universe is the ultimate laboratory to study fundamental physics across energy scales that span about 25 orders of magnitude: from the grand unification scale through particle and nuclear physics scales down to the scale of atomic physics. The standard models of cosmology and particle physics provide the basic understanding of the early and present Universe and predict a series of phase transitions that occurred in succession during the expansion and cooling history of the Universe. We survey these phase transitions, highlighting the equilibrium and non-equilibrium effects as well as their observational and cosmological consequences. We discuss the current theoretical and experimental programs to study phase transitions in QCD and nuclear matter in accelerators along with the new results on novel states of matter as well as on multi- fragmentation in nuclear matter. A critical assessment of similarities and differences between the conditions in the early universe and those in ultra- relativistic heavy ion collisions is presented. Cosmological observations and accelerator experiments are converging towards an unprecedented understanding of the early and present Universe., Comment: 41 pages, 16 figures, to appear in Ann. Rev. Nucl. Part. Sci 2006. Presentation improved, references added

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop MonteCarlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense object for eta > eta_T in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at eta = eta_T. We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension 1 < D < 3., Comment: 12 pages, Invited lecture at `Statistical Mechanics of Non-Extensive Systems', Observatoire de Paris, October 2005, to be published in a Special issue of `Les Comptes rendus de l'Acade'mie des sciences', Elsevier

Slow-roll inflation can be studied as an effective field theory. The form of the inflaton potential consistent with the data is V(phi) = N M^4 w(phi/[sqrt{N} M_{Pl}]) where phi is the inflaton field, M is the inflation energy scale, and N ~ 50 the number of efolds. The dimensionless function w(chi) and field chi are O(1). This form of the potential encodes the slow-roll expansion as an expansion in 1/N.A The Hubble parameter, inflaton mass and non-linear couplings are of the see-saw form in terms of M/M_{Pl}. The quartic coupling is lambda~1/N (M/M_{Pl})^4. The smallness of the non-linear couplings is not a result of fine tuning but a natural consequence of the validity of the effective field theory and slow roll approximation. Quantum corrections to slow roll inflation are computed and turn to be an expansion in powers (H/M_{Pl})^2. The corrections to the inflaton effective potential and its equation of motion are computed, as well as the quantum corrections to the observable power spectra. The near scale invariance of the fluctuations introduces a strong infrared behavior naturally regularized by Delta=(n_s -1)/2+r/8. We consider scalar curvature and tensor perturbations as well as light scalars and Dirac fermions coupled to the inflaton.The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. This inflationary effective potential is strikingly different from the usual Minkowski space-time result.Quantum corrections to the power spectra are expressed in terms of the CMB observables. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations., Comment: 20 pages, 1 figure, Opening Lecture at JGRG15 Tokyo, Japan, November 2005. Lecture at Miami05, Key Biscayne, Florida, December 2005

We consider the QCD scattering amplitudes at high energies sqrt{s} and fixed momentum transfers sqrt{-t} in the leading logarithmic approximation at a non-zero temperature T in the t-channel. It is shown that the BFKL Hamiltonian has the property of holomorphic separability. The holomorphic Hamiltonian for n-reggeized gluons at temperature T is shown to be obtained from the T=0 Hamiltonian by an unitary transformation. The connection with field quantization in accelerated frames and black hole backgrounds is discussed. The effect of the running of alpha_{QCD} on the pomeron eigenvalues is investigated., Comment: Four pages, no figures. Based on talks at the XIth International Conference on Elastic and Diffractive Scattering, Blois May 2005, France and Diffraction 2004, Cala Gonone, Sardinia, Italy

Neutrino oscillations in the early Universe prior to the epoch of primordial nucleosynthesis is studied by implementing real time non-equilibrium field theory methods. We focus on two flavors of Dirac neutrinos, however, the formulation is general. We obtain the equations of motion for neutrino wavepackets of either chirality and helicity in the plasma allowing for CP asymmetry. Contributions non-local in space-time to the self-energy dominate over the asymmetry for $T \gtrsim 3-5 \mathrm{MeV}$ if the lepton and neutrino asymmetries are of the same order as the baryon asymmetry. We find a new contribution which cannot be interpreted as the usual effective potential. The mixing angles and dispersion relations in the medium depend on \emph{helicity}. We find that resonant transitions are possible in the temperature range $ 10 \lesssim T \ll 100 \mathrm{MeV} $. Near a resonance in the mixing angle, the oscillation time scale in the medium as compared to the vacuum is \emph{slowed-down} substantially for small vacuum mixing angle. The time scale of oscillations \emph{speeds-up} for off resonance high energy neutrinos for which the mixing angle becomes vanishingly small. The equations of motion reduce to the familiar oscillation formulae for negative helicity ultrarelativistic neutrinos, but include consistently both the \emph{mixing angle and the oscillation frequencies in the medium}. These equations of motion also allow to study the dynamics of right handed as well as positive helicity neutrinos., Comment: 31 pages 2 figures. Version to appear in Phys. Rev. D

Slow-roll inflation is studied as an effective field theory.We find as consistent form of the inflaton potential V(phi)=N M^4 w(phi/[sqrt{N}M_P]) where phi is the inflaton field, M the inflation energy scale, M_P the Planck mass, and N~50 the number of efolds since the relevant modes exited the horizon till the end of inflation. The dimensionless function w(chi) and field chi are O(1). The WMAP value for the amplitude of scalar adiabatic fluctuations |\Delta_{k ad}^(S)| fixes the inflation scale M ~ 0.77 10^16 GeV precisely at the GUT scale. This general form of the potential makes manifest that the slow roll expansion is an expansion in 1/N. Powers of 1/N count the orders in the slow roll expansion.This form of the inflaton potential suggests that the super symmetry breaking scale is at the inflation and GUT scales.A Ginzburg-Landau realization of this inflaton potential reveals that Hubble, inflaton mass and non-linear couplings are of the see-saw form in terms of the small ratio M/M_P. For example, the quartic coupling lambda ~ 1/N (M/M_P)^4.The smallness of the non-linear couplings is not a result of fine tuning but a natural consequence of the validity of the effective field theory. We clarify the Lyth bound which relates the tensor/scalar ratio and the value of phi/M_P.Effective field theory is valid for V(phi)<

We obtain the effective inflaton potential during slow roll inflation by including the one loop quantum corrections to the energy momentum tensor from scalar curvature and tensor perturbations as well as quantum fluctuations from light scalars and light Dirac fermions generically coupled to the inflaton. During slow roll inflation there is a clean and unambiguous separation between superhorizon and subhorizon contributions to the energy momentum tensor. The superhorizon part is determined by the curvature perturbations and scalar field fluctuations: both feature infrared enhancements as the inverse of a combination of slow roll parameters which measure the departure from scale invariance in each case.Fermions and gravitons do not exhibit infrared divergences. The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. The one-loop quantum corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow-roll and in the (H/M_PL)^2 expansion. This study provides a complete assessment of the backreaction problem up to one loop including bosonic and fermionic degrees of freedom. The result validates the effective field theory description of inflation and confirms the robustness of the inflationary paradigm to quantum fluctuations. Quantum corrections to the power spectra are expressed in terms of the CMB observables:n_s, r and dn_s/dln k. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations., Comment: 18 pages, no figures

We provide a complete picture to the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when (N, V) -> infty, keeping N/V^{1/3} fixed. We compute the equation of state (we do not assume it as is customary in hydrodynamics), as well as the energy, free energy, entropy, chemical potential, specific heats, compressibilities and speed of sound; we analyze their properties, signs and singularities. All physical quantities turn out to depend on a single variable eta = G m^2 N /[V^{1/3} T} that is kept fixed in the N -> infty and V -> infty limit. The system is in a gaseous phase for eta < eta_T and collapses into a dense object for eta > eta_T in the CE with the pressure becoming large and negative. At eta \simeq eta_T the isothermal compressibility diverges and the gas collapses. Our Monte Carlo simulations yield eta_T \simeq 1.515. We find that PV/[NT] = f(eta). The function f(eta) has a second Riemann sheet which is only physically realized in the MCE. In the MCE, the collapse phase transition takes place in this second sheet near eta_{MC} = 1.26 and the pressure and temperature are larger in the collapsed phase than in the gaseous phase. Both collapse phase transitions (in the CE and in the MCE) are of zeroth order since the Gibbs free energy has a jump at the transitions., Comment: 33 pages, 16 figures, Lecture given at the 7th. Paris Cosmology Colloquium, Observatoire de Paris, June 11-15, 2002 and at the 9th Course of the International School of Astrophysics `Daniel Chalonge', Palermo, Italy, 7-18 September 2002, NATO ASI. Updated version

Precise cosmological data from WMAP and forthcoming CMB experiments motivate the study of the quantum corrections to the slowroll inflationary parameters.We find the quantum (loop) corrections to the equations of motion of the classical inflaton, its quantum fluctuations and the Friedmann equation in general single field slow roll inflation.We implement a renormalized effective field theory EFT approach based on an expansion in (H/M_{Pl})^2 and slow roll parameters epsilon_V,eta_V,sigma_V, xi_V.We find that the leading order quantum corrections to the inflaton effective potential and its equation of motion are determined by the power spectrum of scalar fluctuations. Its near scale invariance introduces a strong infrared behavior naturally regularized by the slow roll parameter Delta = eta_V-epsilon_V=(n_s-1)/2+r/8.To leading order in the EFT and slow roll expansions we find V_{eff}(Phi_0)=V_R(Phi_0)[1+(Delta^2_T/32)(n_s-1+3r/8) /(n_s-1+r/4)+higher orders]where n_s and r=Delta^2_T/Delta^2_R are the CMB observables that depend implicitly on Phi_0, and V_R(Phi_0) is the renormalized classical inflaton potential.This effective potential during slow roll inflation is strikingly different from the Minkowski space-time result.Superhorizon scalar field fluctuations grow for late times eta -> 0^- as |\eta|^{-1+Delta-d_} where d_ is a novel quantum correction to the scaling exponent related to the self decay of superhorizon inflaton fluctuations eta is the conformal time. We generalize this to the case of the inflaton interacting with a light scalar field. These quantum corrections arising from interactions will compete with higher order slow-roll corrections and must be taken into account for the precision determination of inflationary parameters., Comment: 21 pages, 1 figure

We clarify classical inflaton models by considering them as effective field theories `a la Ginzburg-Landau. In this approach, the WMAP statement excluding the pure phi^4 potential implies the presence of an inflaton mass term at the scale m ~ 10^{13}GeV.Chaotic, new and hybrid inflation models are studied in an unified manner.In all cases the inflaton potential takes the form V(phi)=m^2 M_{Pl}^2 v(phi/M_{Pl}), where all coefficients in v(varphi) are of order one.If such potential corresponds to supersymmetry breaking, the susy scale is sqrt{m M_{Pl}}~10^{16}GeV which coincides with the GUT scale. For red tilted spectrum new inflation turns to be favoured while for blue tilted spectrum, hybrid inflation turns to be the best choice.In both cases, we find an analytic formula relating the inflaton mass with r (tensor/scalar ratio) and the scalar spectral index ns: 10^6 m/M_{Pl} = 127 sqrt{r|1-n_s|} where the numerical coefficient follows from the WMAP amplitude. We review quantum phenomena during inflation which contribute to relevant observables in the CMB anisotropies and polarization and we focus on inflaton decay.The deviation from the scale invariant power spectrum is measured by a small parameter Delta.Delta regulates the infrared divergences too.In slow roll inflation, Delta is a simple function of the slow roll parameters. The quantum fluctuations can selfdecay in the inflationary expansion through processes forbidden in Minkowski. We compute the self-decay of the inflaton quantum fluctuations during slow roll:superhorizon fluctuations decay as eta^{Gamma} in conformal time where the new scaling dimension Gamma is expressed in terms of the amplitude, n_s and r. we discuss the implications for scalar and tensor perturbations as well as for non gaussianities., Comment: 12 pages, Lecture given at `The Density Perturbation in the Universe', Demokritos Center, Athens, Grece, June 2004

The universe cools down monotonically following its expansion.This generates a sequence of phase transitions. If a second order phase transition happens during the radiation dominated era with a charged order parameter, spinodal unstabilities generate large numbers of charged particles. These particles hence produce magnetic fields.We use out of equilibrium field theory methods to study the dynamics in a mean field or large N setup.The dynamics after the transition features two distinct stages: a spinodal regime dominated by linear long wave length instabilities, and a scaling stage in which the non-linearities and backreaction of the scalar fields are dominant. This second stage describes the growth of horizon sized domains. We implement a formulation based on the non equilibrium Schwinger-Dyson equations to obtain the spectrum of magnetic fields that includes the dissipative effects of the plasma. We find that large scale magnetogenesis is efficient during the scaling regime. Charged scalar field fluctuations with wavelengths of the order of the Hubble radius induce large scale magnetogenesis via loop effects.The leading processes are:pair production, pair annihilation and low energy bremsstrahlung, these processes while forbidden in equilibrium are allowed strongly out of equilibrium. The ratio between the energy density on scales larger than L and that in the background radiation r(L,T)= rho_B(L,T)/rho_{cmb}(T) is r(L,T) ~ 10^{-34} at the Electroweak scale and r(L,T) ~ 10^{-14} at the QCD scale for L sim 1 Mpc. The resulting spectrum is insensitive to the magnetic diffusion length and equipartition between electric and magnetic fields does not hold. We conjecture that a similar mechanism could be operative after the QCD chiral phase transition., Comment: 11 pages, no figures. Lecture given at the International Conference Magnetic Fields in the Universe, Angra dos Reis, Brazil, November, 2004