Search

We investigate the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium dynamics is studied by numerically solving the equations of motion in a light- cone-like discretization of the model for a broad range of initial conditions and energy densities.A smooth cascade of energy towards the ultraviolet is found to be the basic mechanism of thermalization.After an initial transient stage,at a time scale of several hundreds inverse masses,the squared of the field gradient becomes larger than the nonlinear term and a stage of universal cascade emerges. As the cascade progresses, the modes with higher wavenumbers exhibit weaker and weaker nonlinearities well described by the Hartree approximation while the infrared modes retain strong selfinteractions. Two timescales for equilibration appears.For k^2>(t) we observe an effective thermalization with a time scale in the thousands of inverse masses and the Hartree approximation holds. By effective thermalization we mean that the observable acquires the equilibrium functional form with an effective time dependent temperature Teff, which slowly decreases with time. Infrared modes with k^2 < (t) equilibrate only by time scales in the millions of inverse masses. Infrared modes with k^2 < (t) equilibrate only by time scales in the millions.Virialization and the equation of state start to set much earlier than effective thermalization.The applicability of these results in quantum field theory for large occupation numbers and small coupling is analyzed., Comment: 47 pages, 31 figures. Presentation improved, 4 new figures

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

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, 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) 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, 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 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., 41 pages, 10 figures, 3 photos. Problem in group photo fixed

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., 22 pages, 3 pictures. Problem with the poster 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)., 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 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., 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 r0.16 (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 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, Comment: 19 pages, 18 figures. Minor additions. Matches version published in Phys. Rev. D

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

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

The non-relativistic self-gravitating gas in thermal equilibrium in the presence of a positive cosmological constant Lambda (dark energy) is investigated. The dark energy introduces a force pushing outward all particles with strength proportional to their distance to the center of mass.We consider the statistical mechanics of the self-gravitating gas of N particles in a volume V at thermal equilibrium in the presence of Lambda. It is shown that the thermodynamic limit exists and is described by the mean field equations provided N, V -> inf with N/V^{1/3} fixed and Lambda V^{2/3} fixed. That is, Lambda -> 0 for N, V -> inf. The case of Lambda fixed and N, V -> inf is solved too. We solve numerically the mean field equation for spherical symmetry obtaining an isothermal sphere for Lambda>0. The particle distribution turns to flatten compared with the Lambda = 0 case.Moreover, the particle density increases with the distance when the cosmological constant dominates. There is a bordering case with uniform density.The density contrast between the center and the boundary is significatively reduced. In addition, the critical point associated to the collapse (Jeans') phase transition is pushed towards higher values of N/[T V^{1/3}] by the presence of Lambda > 0.The nature and the behaviour near the critical points is not affected by the presence of Lambda>0., LaTex, 29 pages, 15 .ps figures. Stability analysis revised and improved

We study the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. We find that the Hartree approximation is remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by numerically solving the equations of motion in light-cone coordinates for a broad range of initial conditions and energy densities.The time evolution is described by several stages with a cascade of energy towards the ultraviolet. After a transient stage, the spatio-temporal gradient terms become larger than the nonlinear term and a stage of universal cascade emerges.This cascade starts at a time scale t_0 independent of the initial conditions (except for very low energy density). Here the power spectra feature universal scaling behavior and the front of the cascade k(t) grows as a power law k(t) sim t^alpha with alpha lesssim 0.25. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium (LTE) with all correlations being determined by the equilibrium functional form with an effective time dependent temperatureTeff(t) which slowly decreases as sim t^{-alpha}.Two well separated time scales emerge while Teff(t) varies slowly, the wavectors in the wake with k < k(t) attain LTE on much shorter time scales.This universal scaling stage ends when the front of the cascade reaches the cutoff at a time t_1 sim a^{-1/alpha}. Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale., relevance for quantum field theory discussed providing validity criteria. To appear in Phys. Rev. D

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 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.

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

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

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., 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

The physics during the inflationary stage of the universe is of quantum nature involving extremely high energy densities. Moreover, it is out of equilibrium on a fastly expanding dynamical geometry. We complement here the 1999 Chalonge Lectures on out of equilibrium fields in self-consistent inflationary dynamics [astro-ph/0006446] investigating inflation driven by the evolution of highly excited quantum states. These states are characterized by a non-perturbatively large number of quanta in a band of momenta and with zero or nonzero expectation value of the inflaton scalar field. They represent the situation in which initially a non-perturbatively large energy density is localized in a band of high energy quantum modes and are coined tsunami-waves. The self- consistent evolution of this quantum state and the scale factor is studied analytically and numerically. It is shown that the time evolution of these quantum states lead to two consecutive stages of inflation under conditions that are the quantum analogue of slow-roll. The evolution of the scale factor during the first stage has new features that are characteristic of the quantum state. During this initial stage the quantum fluctuations in the highly excited band build up an effective homogeneous condensate with a non-perturbatively large amplitude as a consequence of the large number of quanta.The second stage of inflation is similar to the usual classical chaotic scenario but driven by this effective condensate.The excited quantum modes are superhorizon in the first stage and do not affect the power spectrum of scalar perturbations.Thus, this tsunami quantum state provides a field theoretical justification for chaotic scenarios driven by a classical homogeneous scalar field of large amplitude., LaTex, 29 pages, 7 .ps figures, Lectures at the 8th. Erice Chalonge School, p. 45-80 in the Proceedings, edited by H.J. de Vega, I.M. Khalatnikov and N.G. Sanchez, Kluwer 2001

The essential features underlying the top-down scenarii for UHECR are discussed, namely, the stability (or lifetime) imposed to the heavy objects (particles) whatever they be: topological and non-topological solitons, X-particles, cosmic defects, microscopic black-holes, fundamental strings. We provide an unified formula for the quantum decay rate of all these objects as well as the particle decays in the standard model. The key point in the top-down scenarii is the necessity to adjust the lifetime of the heavy object to the age of the universe. This ad-hoc requirement needs a very high dimensional operator to govern its decay and/or an extremely small coupling constant. The natural lifetimes of such heavy objects are, however, microscopic times associated to the GUT energy scale (sim 10^{-28} sec. or shorter). It is at this energy scale (by the end of inflation) where they could have been abundantly formed in the early universe and it seems natural that they decayed shortly after being formed., 11 pages, LaTex, no figures, updated version

We study the Landau pole in the lambda phi^4 field theory at non-zero and large temperatures. We show that the position of the thermal Landau pole Lambda_L(T) is shifted to higher energies with respect to the zero temperature Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0), Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of applicability in energy of the lambda phi^4 field theory increases with the temperature., LaTex, 6 pages, 2 .ps figures. Improved version. To appear in Phys. Rev. D, Rapid Communications

The physics during the inflationary stage of the universe is of quantum nature involving extremely high energy densities. Moreover, it is out of equilibrium on a fastly expanding dynamical geometry.We present in these lectures non-perturbative out of equilibrium field theoretical methods in cosmological universes. We then study the non-linear dynamics of quantum fields in matter and radiation dominated FRW and de Sitter universes. We investigate the explosive particle production due to spinodal instabilities and parametric amplification in FRW and deSitter universes with and without symmetry breaking. We show how the particle production is sensitive to the expansion of the universe.We present a complete renormalization scheme for the equation of motion and the energy momentum tensor in flat cosmologies. We then consider an O(N) inflaton model coupled self-consistently to gravity in the semiclassical approximation, with `new inflation' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. A very specific combination of these large quantum fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. The metric perturbations during inflation are computed using this effective field and the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensorperturbations and find for these models that the spinodal instabilities are responsible for a `red' primordial spectrum., Latex file, 60 pages, 14 figures in .eps files. To appear in the Proceedings of the VIIth. Erice Chalonge School on Astrofundamental Physics, N. S'anchez ed., Kluwer, Series C, 2000

These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the phenomenological approach based on the Time Dependent Ginzburg-Landau (TDGL) description. After a general discussion of the main experimental and theoretical features of phase ordering kinetics and the description of linear (spinodal) instabilities we introduce the scaling hypothesis and show how a dynamical correlation length emerges in the large N limit in condensed matter systems. The large N approximation is a powerful tool in quantum field theory that allows the study of non-perturbative phenomena in a consistent manner. We study the exact solution to the dynamics after a quench in this limit in Minkowski space time and in radiation dominated Friedman-Robertson-Walker Cosmology. There are some remarkable similarities between these very different settings such as the emergence of a scaling regime and of a dynamical correlation length at late times that describe the formation and growth of ordered regions. In quantum field theory and cosmology this length scale is constrained by causality and its growth in time is also associated with coarsening and the onset of a condensate. We provide a density matrix interpretation of the formation of defects and the classicalization of quantum fluctuations., Comment: 23 pages (revtex), 7 eps figures. Lectures delivered at the NATO Advanced Study Institute: Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions

The dynamics of symmetry breaking during out of equilibrium phase transitions is a topic of great importance in many disciplines, from condensed matter to particle physics and early Universe cosmology with definite experimental impact. In these notes we provide a summary of the relevant aspects of the dynamics of symmetry breaking in many different fields with emphasis on the experimental realizations. In condensed matter we address the dynamics of phase ordering, the emergence of condensates, coarsening and dynamical scaling. In QCD the possibility of disoriented chiral condensates of pions emerging during a strongly out of equilibrium phase transition is discussed. We elaborate on the dynamics of phase ordering in phase transitions in the Early Universe, in particular the emergence of condensates and scaling in FRW cosmologies. We mention some experimental efforts in different fields that study this wide ranging phenomena and offer a quantitative theoretical description both at the phenomenological level in condensed matter, introducing the scaling hypothesis as well as at a microscopic level in quantum field theories. The emergence of semiclassical condensates and a dynamical length scale is shown in detail, in quantum field theory this length scale is constrained by causality. The large N limit provides a natural bridge to compare the solutions in different settings and to establish similarities and differences., Comment: 35 pages, Revtex, 10 figures. Invited by the National Academy of Sciences of India, to appear in ANSI-2000

We analyze the non-equilibrium dynamics of the O(N) Phi^4 model in the large N limit and for states of large energy density. The dynamics is dramatically different when the energy density is above the top of the tree level potential V_0 than when it is below it.When the energy density is below V_0, we find that non-perturbative particle production through spinodal instabilities provides a dynamical mechanism for the Maxwell construction. The asymptotic values of the order parameter only depend on the initial energy density and all values between the minima of the tree level potential are available, the asymptotic dynamical `effective potential' is flat between the minima. When the energy density is larger than V_0, the evolution samples ergodically the broken symmetry states, as a consequence of non-perturbative particle production via parametric amplification. Furthermore, we examine the quantum dynamics of phase ordering into the broken symmetry phase and find novel scaling behavior of the correlation function. There is a crossover in the dynamical correlation length at a time scale t_s \sim \ln(1/lambda). For t < t_s the dynamical correlation length ��(t) \propto \sqrt{t} and the evolution is dominated by spinodal instabilities, whereas for t>t_s the evolution is non-linear and dominated by the onset of non-equilibrium Bose-Einstein condensation of long-wavelength Goldstone bosons.In this regime a true scaling solution emerges with a non- perturbative anomalous scaling length dimension z=1/2 and a dynamical correlation length ��(t) \propto (t-t_s). The equal time correlation function in this scaling regime vanishes for r>2(t-t_s) by causality. For t > t_s the equal time correlation function falls of as 1/r. A semiclassical but stochastic description emerges for time scales t > t_s., Minor improvements, to appear in Phys. Rev. D. Latex file, 48 pages, 12 .ps figures

The real time evolution of field condensates is solved for small and large field amplitudes in scalar theories.For small amplitudes,the quantum equations of motion for the condensate can be linearized and solved by Laplace transform. The late time evolution turns to be determined by the singularities in the complex plane (one-particle poles, two- and multi- particle cuts, Landau cuts for non-zero initial temperature). In hot scalar electrodynamics, we solve the real time evolution of field condensates with soft length scales \sim k^{-1}>(eT)^{-1}. Transverse gauge invariant condensates relax as 1/t^2 to amplitudes determined by the quasiparticle poles. We rederive the HTL action using the non-equilibrium field theory techniques.In the nonlinear regime (for large initial energy densities) we analyze the dynamics of dissipation and relaxation in scalar theory after linear unstabilities are shut-off by the quantum back-reaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non-perturbative in the coupling and initial amplitude. A combination of numerical analysis and the implementation of a dynamical renormalization group resummation via multi-time scale analysis reveals the presence of unstable bands in the nonlinear regime. These are associated with power law growth of quantum fluctuations, that result in power law relaxation and dissipation with {\bf non-universal and non-perturbative dynamical anomalous exponents., Latex file, 10 pages, 3 .eps figures. Lecture delivered at TFT98, the Vth International Workshop on Thermal Field Theories and Their Applications, Ratisbona (Regensburg), Germany, 10-14 August 1998

We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background is locally anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelized. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both semi-classical and canonical string-quantization, in order to see the effect of the conformal invariance of the background on the string mass spectrum. Both approaches yield that the high-mass states are governed by m sim HN (N,`large integer'), where m is the string mass and H is the Hubble constant. It follows that the level spacing grows proportionally to N: d(m^2 alpha')/dN sim N, while the entropy goes like: S sim sqrt{m}. Moreover, it follows that there is no Hagedorn temperature,so that the partition function is well defined at any positive temperature. All results are compared with the analogue results in Anti- de Sitter spacetime, which is a non conformal invariant background. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conformal and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal backgrounds are identical. Interestingly enough, conformal invariance fixes the value of the spacetime curvature to be -69/(26 alpha')., Latex file, 23 pages, no figures

The energy and time scales during the inflationary stage of the universe calls for an out of equilibrium quantum field treatment. Moreover, the high energy densities involved make necessary the use of non-perturbative approaches as large N and Hartree methods. We start these lectures by introducing such non-perturbative out of equilibrium methods in cosmological universes. We discuss the renormalization procedure and the choice of initial conditions. We then study the nonlinear dynamics of quantum fields in matter and radiation dominated FRW and de Sitter universes. For a variety of initial conditions, we compute the evolution of the inflaton,its quantum fluctuations and the equation of state. We investigate the explosive particle production due to spinodal unstabilities and parametric amplification in FRW and de Sitter universes with and without symmetry breaking.We find that the particle production is sensitive to the expansion of the universe.For symmetry breaking scenarios, we determine generic late time fields behavior for FRW and deSitter cosmologies.We find that quantum fluctuations damp in FRW as the square of the scale factor while the order parameter approaches a minimum of the potential at the same rate.We con- sider an O(N) inflaton model coupled self-consistently to gravity in the semi- classical approximation for a `new inflation' scenario. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off inflation. These fluctuations assemble with the inflaton zero mode yielding a new effective field that actually rolls down behaving classi- cally. We compute the amplitude and index for scalar density and tensor perturbations. In all models of this type the spinodal instabilities produce a `red' spectrum of primordial scalar density perturbations., Latex file, 76 pages, 26 figures in .eps files. To appear in the Proceedings of the VIth. Erice Chalonge School on Astrofundamental Physics, N. S\'anchez and A. Zichichi eds., Kluwer, 1998

We study photoproduction during the non-equilibrium stages of the formation of chiral condensates within the ``quench'' scenario of the chiral phase transition. The dynamics is modeled with a gauged linear sigma model. A novel quantum kinetic approach to the description of photoproduction far off equilibrium is developed. We find that non-equilibrium spinodal instabilities of long wavelength pion fluctuations are responsible for an enhanced photoproduction rate for energies $\leq 80$ MeV at order $\alpha$. These non-equilibrium effects lead to a larger contribution than the typical processes in the medium, including that of the anomalous neutral pion decay $\pi^0 \rightarrow 2 \gamma$ (which is of order $\alpha^2$). We follow the evolution of the dynamics throughout the phase transition, which in this scenario occurs on a time scale of about $2.5-3$ fm/c and integrate the photon yield through its evolution. The spectrum of photons produced throughout the phase transition is a non- equilibrium one. For thermal initial conditions at the time of the quench it interpolates between a thermal distribution about 6% above the initial temperature (at the time of the quench) for low energy $\leq 80$ MeV photons, and a high energy tail in thermal equilibrium at the initial temperature, with a smooth crossover at 100 MeV. The rate displays a peak at $\sim 35$ MeV which receives a larger enhancement the closer the initial temperature at the time of the quench is to the critical temperature. It is found that the enhancement of photoproduction at low energies is not an artifact caused by the initial distribution of the photons, but is due to the pionic instabilities. We suggest that these strong out of equilibrium effects may provide experimental signatures for the formation and relaxation of DCC's in heavy ion collisions., Comment: 33 pages, 11 figures, uses revtex and epsfig

We study production of photons via the non-equilibrium relaxation of a Disoriented Chiral Condensate with the chiral order parameter having a large initial amplitude along the ��^0 direction. Assuming the validity of the low energy coupling of the neutral pion to photons via the U_A(1) anomalous vertex, we find that for large initial amplitudes along the ��^0 direction, photon production is enhanced by parametric amplification. These processes are non-perturbative with a large contribution during the non-equilibrium stages of the evolution and result in a distinct distribution of the produced photons and a polarization asymmetry. For initial amplitudes of the ��^0 component of the order parameter between 200-400 MeV, corresponding to energy densities between 1-12 GeV/fm^3 we find a peak in the photon distribution at energies between \approx 300 -600 MeV. We also find polarization asymmetries typically between 5-10%. We discuss the potential experimental impact of these results as well as the problems associated with its detection., 36 pages, 14 figures, uses revtex

Recent progress in the preheating phenomena for inflationary cosmology is reviewed. We first discuss estimates of the preheating time scale and particle production at the early stages of parametric amplification within the Mathieu and Lam'e approximations and we analyze their precision and limitations. The necessity of self-consistent calculations including the non-linearity of the field theory equations in an energy conserving scheme is stressed. The large N calculations including the field back-reaction are reviewed. For spontaneously broken theories the issue of symmetry restoration is analyzed. A discussion of the possibility and criterion for symmetry restoration is presented., Latex file, expanded (+50%) and improved version, eight pages and thirteen .ps figures. To appear in the Proceedings of the Paris Euronetwork Meeting `String Gravity'

The quantum energy-momentum tensor ${\hat T}^{\mu\nu}(x)$ is computed for strings in Minkowski space-time. We compute its expectation value for different physical string states both for open and closed bosonic strings. The states considered are described by normalizable wave-packets in the center of mass coordinates. We find in particular that ${\hat T}^{\mu\nu}(x)$ is {\bf finite} which could imply that the classical divergence that occurs in string theory as we approach the string position is removed at the quantum level as the string position is smeared out by quantum fluctuations. For massive string states the expectation value of ${\hat T}^{\mu\nu}(x)$ vanishes at leading order (genus zero). For massless string states it has a non-vanishing value which we explicitly compute and analyze for both spherically and cylindrically symmetric wave packets. The energy-momentum tensor components propagate outwards as a massless lump peaked at $ r = t $., Comment: Latex, 15 pages

The nonlinear time evolution of the quantum fields is studied in the O(N) model for large N in a radiation dominated FRW universe, with a view towards the phenomenon of explosive particle production due to either spinodal instabilities or parametric amplification, i.e. preheating. Quantum backreaction effects due to the produced particles are included consistently within the large N approximation. We find that preheating persists when the expansion is included, although the amount of particle production is reduced compared to the values found in Minkowski space. We also see that the behavior of the evolving zero mode is very different from that in Minkowski space, though the late time behavior in all cases is determined by a sum rule that implies the existence of Goldstone bosons in the final state., Comment: 6 pages, RevTex, 2 epsf figures

Reply to the comment by L. Kofman, A. Linde and A.A. Starobinsky (hep-ph/9608341) to our article ``Analytic and Numerical Study of Preheating Dynamics'' (hep-ph/9608205)., Comment: 5 pages, revtex

Recent progress on string theory in curved spacetimes is reviewed. The string dynamics in cosmological and black hole spacetimes is investigated.The methods to solve the string equations of motion in curved spacetimes are described.That is, the perturbation approach, the null approach, the $\tau$-expansion, and the construction of global solutions.The behaviour of strings in FRW and inflatio- nary spacetimes is obtained from the various types of string solutions. Three different types of behaviour appear:{\bf unstable, dual} to unstable and {\bf stable}.For the unstable strings, the energy and size grow proportional to $R$ for large scale factors $R \to \infty$. For the dual to unstable strings, the energy and size blow up for R\to 0 as 1/R. For stable strings, the energy and size are bounded. (In Minkowski, all solutions are of the stable type). The self-consistent solution to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is taken as source and from the above behaviours the string equation of state is {\bf derived}. The self-consistent string solution exhibits realistic matter dominated behaviour for large times and radiation dominated behaviour for early times. We report on the {\bf exact integrability} of the string dynamics in de Sitter spacetime that allows to systematically find {\bf exact} string solutions by soliton methods. {\bf Multistring solutions} are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows from the coupling of the strings with the geometry. Finally, the string dynamics next and inside a Schwarzschild black hole is analyzed and their physical properties discussed., Comment: 55 pages, Based on lectures delivered at the Third Paris Cosmology Colloquium, Observatoire de Paris 7 - 9 June 1995, and at the Erice Chalonge School, `String Gravity and Physics at the Planck Scale', 8-19 September 1995. Figures available from the authors

We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and the study the relaxation of the inflaton via particle production in both the linear and non-linear regimes. This has an immediate application to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and thermalization. We find that particle production when the inflaton starts in the {\it non-linear} region is typically a far more efficient way of transfering energy out of the inflaton zero mode and into the quanta of the lighter scalar than single particle decay. For the non-linear regime we take into account self-consistently the evolution of the expectation value of the inflaton field coupled to the evolution of the quantum fluctuations. An exhaustive numerical analysis reveals that the distribution of produced particles is far from thermal, and the effect of open channels. In the fermionic case, Pauli blocking begins to hinder the transfer of energy into the fermion modes very early on in the evolution of the inflaton. We examine the implications of our results to the question of how to calculate the reheating temperature of the universe after inflation., Revtex 3.0; 34 pages

We consider the non-equilibrium evolution of the inflaton field coupled to both lighter scalars and fermions. The dissipational dynamics of this field is studied and found to be quite different than that believed in inflationary models. In particular, the damping time scale for the expectation value of the zero momentum mode of the inflaton can be much shorter than that given by the single particle decay rate when the inflaton amplitudes are large, as in chaotic inflation scenarios. We find that the reheating temperature may depart considerably from the usual estimates., 9 pages, revtex 3.0, 3 figures available upon request

The reheating stage in post-inflationary cosmologies is reanalyzed. New techniques from non-equilibrium quantum field theory allow a consistent derivation of the equation of motion including the non-linearity of the dynamics. These offer a rationale for the elementary theory of reheating based on single particle decay which is seen to be valid only in the linear regime of coherent oscillations of the scalar field. A new non-perturbative mechanism of induced amplification of quantum fluctuations is introduced and studied in detail, both analytically and numerically. This is a non-linear mechanism that is typically a far more efficient way of transfering energy out of the zero mode and into production of lighter particles than single particle decay. Thermalization is discussed and we estimate the reheating temperature to be of the order of the inflaton mass, thus providing a potential solution to the Polonyi and moduli problems., Comment: To appear in the Proceedings of the School on String Gravity and Physics at the Planck Scale, Erice, Sicily, 8-19 September, Editor: N. Sanchez, Revtex, 39 pages, 9 figures available upon request

Progress on string theory in curved spacetimes since 1992 are reviewed. After a short introduction on strings in Minkowski and curved spacetimes, we focus on strings in cosmological spacetimes. The classical behaviour of strings in FRW and inflationary spacetimes is now understood in a large extent from various types of explicit string solutions. Three different types of behaviour appear in cosmological spacetimes: {\bf unstable, dual} to unstable and {\bf stable}. For the unstable strings, the energy and size grow for large scale factors $R \to \infty$, proportional to $R$. For the dual to unstable strings, the energy and size blow up for $R\to 0$ as $1/R$. For stable strings, the energy and proper size are bounded. (In Minkowski spacetime, all string solutions are of the stable type).Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is determined. The self-consistent string solution exhibits the realistic matter dominated behaviour $R \sim (X^0)^{2/3}\; $ for large times and the radiation dominated behaviour $R \sim (X^0)^{1/2}\;$ for early times. Finally, we report on the exact integrability of the string equations plus the constraints in de Sitter spacetime that allows to systematically find {\bf exact} string solutions by soliton methods and the multistring solutions. {\bf Multistring solutions} are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows to the coupling of the strings with the geometry., Comment: A few minor corrections. Lectures delivered at the Erice School `Current Topics in Astrofundamental Physics', 4-16 September 1994, 42 pages, LaTex. Figures available from the authors

The exact general solution of circular strings in $2+1$ dimensional de Sitter spacetime is described completely in terms of elliptic functions. The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. This has no analogue in flat spacetime. The circular strings are either oscillating ("stable") or indefinitely expanding ("unstable"). We then compute the {\it exact} equation of state of circular strings in the $2+1$ dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. We finally perform a semi-classical quantization of the oscillating circular strings. We find the mass formula $\alpha'm^2_{\mbox{dS}}\approx 4n-5H^2\alpha'n^2,\;(n\in N_0),$ and a {\it finite} number of states $N_{\mbox{dS}}\approx 0.34/(H^2\alpha')$ in de Sitter spacetime; $m^2_{\mbox{AdS}}\approx H^2n^2$ (large $n\in N$) and $N_{\mbox{AdS}}=\infty$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime., Comment: Latex, 19 pages + 6 figures and 3 tables (not included). To appear in "New Developments in string gravity and physics at the Planck energy scale" (World Scientific, Singapore, 1995)

This is a short review on strings in curved spacetimes. We start by recalling the classical and quantum string behaviour in singular plane waves backgrounds. We then report on the string behaviour in cosmological spacetimes (FRW, de Sitter, power inflation) which is by now largerly understood. Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is considered as source of the spacetime geometry. The string equation of state is determined from the behaviour of the explicit string solutions. This yields a self-consistent cosmological solution exhibiting realistic matter dominated behaviour $ R \sim (T)^{2/3}\; $ for large times and radiation dominated behaviour $ R \sim (T)^{1/2}\; $ for early times. Inflation in the string theory context is discussed., Comment: Lecture delivered at STRINGS '95, Future Perspectives in String Theory, USC, Los Angeles, march 13 - 18, 1995, 12 pages, LaTex

The light-cone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through the Bethe Ansatz. We show here how to derive the infinite number of local commuting and non-local and non-commuting conserved charges in integrable QFT, taking the massive Thirring model (sine-Gordon) as an example. They are generated by quantum monodromy operators and provide a representation of $q-$deformed affine Lie algebras $U_q({\hat\G})$. Based on lectures delivered at the $XXX_q$ Karpacz Winter School, Poland, February 14-26, 1994., 21 pages, Latex, LPTHE preprint 94-26. Figures available from the author under request

We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. After setting the problem in general we propose a non-perturbative, self-consistent Hartree approximation. The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. The infinite time limit is computed for de Sitter spacetime. We obtain the time evolution of the initial Boltzmann distribution functions, and argue that in the Hartree approximation, the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by studying the case of a free field in de Sitter and radiation dominated cosmologies. It is found that a suitably defined non-equilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is {\it not} a monotonically increasing function in the radiation dominated case. This work has been done in collaboration with D. Boyanovsky and R. Holman., 14 pages, Latex, LPTHE 94-20

In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the new inflationary models, we show that the instabilities that are the hallmark of the phase transition, that is the formation of correlated domains, dramatically change this picture. We analyze in detail the dynamics of phase separation in strongly supercooled phase transitions in Minkowski space. We argue that this is typically the situation in weakly coupled scalar theories. The effective evolution equations for the expectation value and the fluctuations of an inflaton field in a FRW cosmology are derived both in the loop expansion and in a self-consistent non-perturbative scheme. Finally we use these non-equilibrium techniques and concepts to study the influence of quantum and thermal fluctuations on the dynamics of a proposed mechanism for the formation of disoriented chiral condensates during a rapid phase transition out of equilibrium. This last topic may prove to be experimentally relevant at present accelerator energies. To appear in the Proceedings of the `2nd. Journ\'ee Cosmologie', Observatoire de Paris, 2-4, June 1994. H J de Vega and N. S\'anchez, Editors, World Scientific., Comment: 72 pages, LaTex, Figures availables from the authors upon request

This is a review on infinite non-abelian symmetries in two-dimensional field theories. We show how any integrable QFT enjoys the existence of infinitely many {\bf conserved} charges. These charges {\bf do not commute} between them and satisfy a Yang--Baxter algebra. They are generated by quantum monodromy operators and provide a representation of $q-$deformed affine Lie algebras $U_q({\hat\G})$. We review the work by de Vega, Eichenherr and Maillet on the bootstrap construction of the quantum monodromy operators in classically scale invariant theories where the classical monodromy matrix is conserved. Then, the recent generalization to the sine--Gordon (or massive Thirring) model, where such operators do not possess a classical analogue is given (This provides a representation of $S{\hat U}(2)_q$). It is then reported on the recent work by Destri and de Vega, where both commuting and non-commuting integrals of motion are systematically obtained by Bethe Ansatz in the light-cone approach. The eigenvalues of the six--vertex alternating transfer matrix $\tau(\l)$ are explicitly computed on a generic physical state through algebraic Bethe ansatz. In the thermodynamic limit $\tau(\l)$ turns out to be a two--valued periodic function. One determination generates the local abelian charges, including energy and momentum, while the other yields the abelian subalgebra of the (non--local) YB algebra. In particular, the bootstrap results coincide with the ratio between the two determinations of the lattice transfer matrix.[Based on a Lecture at the Clausthal Symposium]., Comment: 38 pages,uses phyzzx, figures available under request, LPTHE-PAR 93/36

The dynamics of typical phase transitions is studied out of equilibrium in weakly coupled inflaton-type scalar field theories in Minkowski space. The shortcomings of the effective potential and equilibrium descriptions are pointed out. A case of a rapid supercooling from $T_i>T_c$ to $T_f \ll T_c$ is considered. The equations of motion up to one-loop for the order parameter are obtained and integrated for the case of ``slow rollover initial conditions''. It is shown that the instabilities responsible for the process of phase separation introduce dramatic corrections to the evolution. Domain formation and growth (spinodal decomposition) is studied in a non-perturbative self-consistent approximation. For very weakly coupled theories domains grow for a long time, their final size is several times the zero temperature correlation length. For strongly coupled theories the final size of the domains is comparable to the zero temperature correlation length and the transition proceeds faster. We also obtain the evolution equations for the order parameter and the fluctuations to one-loop order and in a non-perturbative Hartree approximation in spatially flat FRW cosmologies. The renormalization, and leading behavior of the high temperature limit are analyzed., 26 pages;Latex;4 figures not included, available upon request; PITT-93-9

The string propagation in the two-dimensional stringy black-hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the lorentzian and euclidean regimes. In the lorentzian case all the physics reduces to a massless scalar particle described by a Klein-Gordon type equation with a singular effective potential. The scattering matrix is found and it reproduces the results obtained by coset CFT techniques. It factorizes into two pieces : an elastic coulombian amplitude and an absorption part. In both parts, an infinite sequence of imaginary poles in the energy appear. The generic features of string propagation in curved D-dimensional backgrounds (string stretching, fall into spacetime singularities) are analyzed in the present case. A new physical phenomenon specific to the present black-hole is found : the quantum renormalization of the speed of light. We find $c_{quantum} = \sqrt{{k\o{k-2}}}~c_{classical}$, where $k$ is the integer in front of the WZW action. This feature is, however, a pathology. Only for $ k \to \infty$ the pathology disappears (although the conformal anomaly is present). We analyze all the classical euclidean string solutions and exactly compute the quantum partition function. No critical Hagedorn temperature appears here., Comment: 32 pages, uses phyzzx

Progress on the physics of strings in curved spacetime are comprehensively reviewed.We start by showing through renormalization group arguments that a meaningful quantum theory of gravity must be finite and must include all particle physics.Then, we review classical and quantum string propagation in curved spacetimes.We start by the general expansion method proposed by de Vega and S\'anchez in 1987. The particle transmutation phenomena in asymptotically flat spacetimes are detailed including fermion-boson transitions in supergravity backgrounds.The next chapters review the exactly solvable cases of string propagation: shock waves, singular plane waves, conical spacetimes and de Sitter cosmological spacetime. The calculation of various physical quantities like the string mass and the energy-momentum tensor shows that classical and quantum string propagation in shock-waves and singular plane waves is physically meaningful and full of interesting new phenomena.The important phenomenom of {\bf string stretching} that takes place when strings fall into spacetime singularities and in expanding universes is analyzed.We conclude by reporting on strings in de Sitter spacetime, where the string equations are integrable and reduce to the sinh-Gordon equation and to integrable generalizations of it. Lectures delivered at the ERICE SCHOOL ``STRING QUANTUM GRAVITY AND PHYSICS AT THE PLANCK ENERGY SCALE'', 21-28 June 1992 , to appear in the Proceedings edited by N. S\'anchez, World Scientific., Comment: 42 pages,uses phyzzx, LPTHE-PAR 92/50 (ERICE lectures)

We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single} non--linear integral equation from which the free energy can be exactly calculated. The high--temperature expansion follows in a sistematic and relatively simple way. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around $T=0$. Furthermore, we derive a single non-linear integral equation describing the finite--size ground--state energy of the Sine--Gordon quantum field theory. PACS: 05.30, 03.70. 75.10.5, 11 pages

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear integral equation from which the free energy can be exactly calculated.These equations are shown to be equivalent to an infinite set of algebraic equations of Bethe type which provide alternatively the thermodinamics. The high-temperature expansion follows in a sistematic and relatively simple way from our non-linear integral equations. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around T=0. Furthermore, we derive a single non-linear integral equation describing the finite-size ground-state energy of the Sine-Gordon quantum field theory., Comment: 12 pages, phyzzx