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Explaining the origin of supermassive black holes via a primordial origin is severely challenged by the tight spectral distortion constraints on the amplitude of the primordial perturbations. Following the first calculation of how the $\mu$ constraints are modified by non-Gaussianity in a companion paper, we here make the first robust constraints on primordial black hole formation under large non-Gaussianity. Even the infinite $f_{\rm NL}$ limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form ${\cal R}={\cal R}_{\rm G}^5$ may allow the formation of any mass primordial black hole without conflicting with distortion constraints. We caution that such extreme models face other challenges., Comment: 24 pages, 6 figures. v2: Minor typos corrected and references added to match the published version

We present an updated analysis of eleven cosmological models that may help reduce the Hubble tension, which now reaches the $6\sigma$ level when considering the latest SH0ES measurement versus recent CMB and BAO data, assuming $\Lambda$CDM. Specifically, we look at five classical extensions of $\Lambda$CDM (with massive neutrinos, spatial curvature, free-streaming or self-interacting relativistic relics, or dynamical dark energy) and six elaborate models featuring either a time-varying electron mass, early dark energy or some non-trivial interactions in the neutrino sector triggered by a light Majoron. We improve over previous works in several ways. We include the latest data from the South Pole Telescope as well as the most recent measurement of the Hubble rate by the SH0ES collaboration. We treat the summed neutrino mass as a free parameter in most of our models, which reveals interesting degeneracies and constraints. We define additional metrics to assess the potential of a model to reduce or even solve the Hubble tension. We validate an emulator that uses active learning to train itself during each parameter inference run for any arbitrary model. We find that the time-varying electron mass and the Majoron models are now ruled out at more than $3\sigma$. Models with a time-varying electron mass and spatial curvature or with early dark energy reduce the tension to $1.0-2.9\sigma$. Nevertheless, none of the models considered in this work is favored with enough statistical significance to become the next concordance model of Cosmology., Comment: 53 pages, 15 figures. Matches accepted version in JCAP

The anisotropies of the Cosmological Gravitational Wave Background (CGWB) retain information about the primordial mechanisms that source the gravitational waves and about the geometry and the particle content of the universe at early times. In this work, we discuss in detail the computation of the angular power spectra of CGWB anisotropies and of their cross correlation with Cosmic Microwave Background (CMB) anisotropies, assuming different processes for the generation of these primordial signals. We present an efficient implementation of our results in a modified version of CLASS which will be publicly available. By combining our new code GW_CLASS with MontePython, we forecast the combined sensitivity of future gravitational wave interferometers and CMB experiments to the cosmological parameters that characterize the cosmological gravitational wave background., Comment: 64 pages, 16 figures. V2 matches the version published by JCAP. GW_CLASS is publicly available on the class_public git repository as a branch GW_CLASS, https://github.com/lesgourg/class_public/tree/GW_CLASS (For details on installation and usage, follow the instructions in the README.)

Spectral distortions and anisotropies of the CMB provide independent and complementary probes to study energy injection processes in the early universe. Here we discuss the synergy between these observables, and show the promising future of spectral distortion missions to constrain both exotic and non-exotic energy injections. We show that conventional probes such as Big Bang Nucleosynthesis and CMB anisotropies can benefit from and even be surpassed by future spectral distortion experiments. For this, we have implemented a unified framework within the Boltzmann code CLASS to consistently treat the thermal evolution of photons and baryons. Furthermore, we give an extensive and pedagogical introduction into the topic of spectral distortions and energy injections throughout the thermal history of the universe, highlighting some of their unique features and potential as a novel probe for cosmology and particle physics., Comment: 62 pages with 10 figures

This paper discusses the science case for a sensitive spectro-polarimetric survey of the microwave sky. Such a survey would provide a tomographic and dynamic census of the three-dimensional distribution of hot gas, velocity flows, early metals, dust, and mass distribution in the entire Hubble volume, exploit CMB temperature and polarisation anisotropies down to fundamental limits, and track energy injection and absorption into the radiation background across cosmic times by measuring spectral distortions of the CMB blackbody emission. In addition to its exceptional capability for cosmology and fundamental physics, such a survey would provide an unprecedented view of microwave emissions at sub-arcminute to few-arcminute angular resolution in hundreds of frequency channels, a data set that would be of immense legacy value for many branches of astrophysics. We propose that this survey be carried-out with a large space mission featuring a broad-band polarised imager and a moderate resolution spectro-imager at the focus of a 3.5m aperture telescope actively cooled to about 8K, complemented with absolutely-calibrated Fourier Transform Spectrometer modules observing at degree-scale angular resolution in the 10-2000 GHz frequency range. We propose two observing modes: a survey mode to map the entire sky as well as a few selected wide fields, and an observatory mode for deeper observations of regions of specific interest., Comment: 20 pages, white paper submitted in answer to the "Voyage 2050" call to prepare the long term plan in the ESA science programme

Many attempts to solve the Hubble tension with extended cosmological models combine an enhanced relic radiation density, acting at the level of background cosmology, with new physical ingredients affecting the evolution of cosmological perturbations. Several authors have pointed out the ability of combined Baryon Acoustic Oscillation (BAO) and Big Bang Nucleosynthesis (BBN) data to probe the background cosmological history independently of both CMB maps and supernovae data. Using state-of-the-art assumptions on BBN, we confirm that combined BAO, deuterium, and helium data are in tension with the SH0ES measurements under the $\Lambda$CDM assumption at the 3.2$\sigma$ level, while being in close agreement with the CMB value. We subsequently show that floating the radiation density parameter $N_\mathrm{eff}$ only reduces the tension down to the 2.6$\sigma$ level. This conclusion, totally independent of any CMB data, shows that a high $N_\mathrm{eff}$ accounting for extra relics (either free-streaming or self-interacting) does not provide an obvious solution to the crisis, not even at the level of background cosmology. To circumvent this strong bound, (i) the extra radiation has to be generated after BBN to avoid helium bounds, and (ii) additional ingredients have to be invoked at the level of perturbations to reconcile this extra radiation with CMB and LSS data., Comment: 17 pages, 5 figures; v2: minor rephrasing and extra references

Reionisation blurring is a non-linear correction to the cosmic microwave background that acts similar to weak gravitational lensing and that can be computed from linear perturbations through a blurring potential. Its impact on the cosmic microwave background is roughly two order of magnitude smaller than that of lensing, in isolation. But the blurring potential is strongly correlated with the lensing potential thereby generating a potentially observable cross-correlation. We compute for the first time the inclusive impact of reionisation blurring on the temperature angular power spectrum and discuss how much it could induce lensing anomalies, Comment: 19 pages, 4 figures, uses jcappub. Discussions and references added, matches published version

We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA's fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume LCDM as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base LCDM, which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. (ABRIDGED), Comment: 90 pages, 25 Figures. Revised version with new authors list and references

We present the public version of hi_class (www.hiclass-code.net), an extension of the Boltzmann code CLASS to a broad ensemble of modifications to general relativity. In particular, hi_class can calculate predictions for models based on Horndeski's theory, which is the most general scalar-tensor theory described by second-order equations of motion and encompasses any perfect-fluid dark energy, quintessence, Brans-Dicke, $f(R)$ and covariant Galileon models. hi_class has been thoroughly tested and can be readily used to understand the impact of alternative theories of gravity on linear structure formation as well as for cosmological parameter extraction., Comment: 17 pages + appendices, 4 figures, code available on https://github.com/miguelzuma/hi_class_public

We estimate the sensitivity of future galaxy surveys to cosmological parameters, using the redshift dependent angular power spectra of galaxy number counts, $C_\ell(z_1,z_2)$, calculated with all relativistic corrections at first order in perturbation theory. We pay special attention to the redshift dependence of the non-linearity scale and present Fisher matrix forecasts for Euclid-like and DES-like galaxy surveys. We compare the standard $P(k)$ analysis with the new $C_\ell(z_1,z_2)$ method. We show that for surveys with photometric redshifts the new analysis performs significantly better than the $P(k)$ analysis. For spectroscopic redshifts, however, the large number of redshift bins which would be needed to fully profit from the redshift information, is severely limited by shot noise. We also identify surveys which can measure the lensing contribution and we study the monopole, $C_0(z_1,z_2)$., Comment: 26 pages, 11 figures; few typos in published version corrected

The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density field is very close to the linear density power spectrum, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor- series expansion we use of the logarithmic mapping. This approach allows us to handle the critical issue of density smoothing in a straightforward way. We also compare our perturbative results with simulation measurements., Comment: Minor clarifications to match version accepted in ApJ. 15 pages, 10 figures

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters., Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references added

We update constraints on the Hubble function H(phi) during inflation, using the most recent cosmic microwave background (CMB) and large scale structure (LSS) data. Our main focus is on a comparison between various commonly used methods of calculating the primordial power spectrum via analytical approximations and the results obtained by integrating the exact equations numerically. In each case, we impose naive, minimally restrictive priors on the duration of inflation. We find that the choice of priors has an impact on the results: the bounds on inflationary parameters can vary by up to a factor two. Nevertheless, it should be noted that within the region allowed by the minimal prior of the exact method, the accuracy of the approximations is sufficient for current data. We caution however that a careless minimal implementation of the approximative methods allows models for which the assumptions behind the analytical approximations fail, and recommend using the exact numerical method for a self-consistent analysis of cosmological data., Comment: 16 pages, 3 figures

We derive new constraints on the Hubble function H(phi) and subsequently on the inflationary potential V(phi) from WMAP 3-year data combined with the Sloan Luminous Red Galaxy survey (SDSS-LRG), using a new methodology which appears to be more generic, conservative and model-independent than in most of the recent literature, since it depends neither on the slow-roll approximation, nor on any extrapolation scheme for the potential beyond the observable e-fold range, nor on additional assumptions about initial conditions for the inflaton velocity. This last feature represents the main improvement of this work, and is made possible by the reconstruction of H(phi) prior to V(phi). Our results only rely on the assumption that within the observable range, corresponding to ~ 10 e-folds, inflation is not interrupted and the function H(phi) is smooth enough for being Taylor-expanded at order one, two or three. We conclude that the variety of potentials allowed by the data is still large. However, it is clear that the first two slow-roll parameters are really small while the validity of the slow-roll expansion beyond them is not established., Comment: 5 pages, 3 figures. Numerical module available at http://wwwlapp.in2p3.fr/~valkenbu/inflationH/ . References added, discussion expanded

We derive some new constraints on single-field inflation from the Wilkinson Microwave Anisotropy Probe 3-year data combined with the Sloan Luminous Red Galaxy survey. Our work differs from previous analyses by focusing only on the observable part of the inflaton potential, or in other words, by making absolutely no assumption about extrapolation of the potential from its observable region to its minimum (i.e., about the branch of the potential responsible for the last ~50 inflationary e-folds). We only assume that inflation starts at least a few e-folds before the observable Universe leaves the Hubble radius, and that the inflaton rolls down a monotonic and regular potential, with no sharp features or phase transitions. We Taylor-expand the inflaton potential at order v=2, 3 or 4 in the vicinity of the pivot scale, compute the primordial spectra of scalar and tensor perturbations numerically and fit the data. For v>2, a large fraction of the allowed models is found to produce a large negative running of the scalar tilt, and to fall in a region of parameter space where the second-order slow-roll formalism is strongly inaccurate. We release a code for the computation of inflationary perturbations which is compatible with CosmoMC., Comment: 10 pages, 6 figures, codes available at http://wwwlapp.in2p3.fr/~lesgourgues/inflation/. Version to be published in Phys.Rev. D

The Fisher matrix formalism has in recent times become the standard method for predicting the precision with which various cosmological parameters can be extracted from future data. This approach is fast, and generally returns accurate estimates for the parameter errors when the individual parameter likelihoods approximate a Gaussian distribution. However, where Gaussianity is not respected (due, for instance, to strong parameter degeneracies), the Fisher matrix formalism loses its reliability. In this paper, we compare the results of the Fisher matrix approach with those from Monte Carlo simulations. The latter method is based on the publicly available CosmoMC code, but uses synthetic realisations of data sets anticipated for future experiments. We focus on prospective cosmic microwave background (CMB) data from the Planck satellite, with or without CMB lensing information, and its implications for a minimal cosmological scenario with eight parameters and an extended model with eleven parameters. We show that in many cases, the projected sensitivities from the Fisher matrix and the Monte Carlo methods differ significantly, particularly in models with many parameters. Sensitivities to the neutrino mass and the dark matter fraction are especially susceptible to change., Comment: 19 pages, 6 figures, our codes are available at http://lappweb.in2p3.fr/~perotto/FUTURCMB/home.html

The next generation of CMB experiments should get a better handle on cosmological parameters by mapping the weak lensing deflection field, which is separable from primary anisotropies thanks to the non-Gaussianity induced by lensing. However, the generation of perturbations in the Early Universe also produces a level of non-Gaussianity which is known to be small, but can contribute to the anisotropy trispectrum at the same level as lensing. In this work, we study whether the primordial non-Gaussianity can mask the lensing statistics. We concentrate only on the ``temperature quadratic estimator'' of lensing, which will be nearly optimal for the Planck satellite, and work in the flat-sky approximation. We find that primordial non-Gaussianity contaminates the deflection field estimator by roughly (0.1 f_NL)% at large angular scales, which represents at most a 10% contribution, not sufficient to threaten lensing extraction, but enough to be taken into account., Comment: 5 pages, 1 figure

Generic models for the origin of structure predict a spectrum of initial fluctuations with a mixture of adiabatic and isocurvature perturbations. Using the observed anisotropies of the cosmic microwave backgound, the matter power spectra from large scale structure surveys and the luminosity distance vs redshift relation from supernovae of type Ia, we obtain strong bounds on the possible cold dark matter/baryon as well as neutrino isocurvature contributions to the primordial fluctations in the Universe. Neglecting the possible effects of spatial curvature and tensor perturbations, we perform a Bayesian likelihood analysis with thirteen free parameters, including independent spectral indexes for each of the modes and for their cross-correlation angle. We find that around a pivot wavenumber of k=0.05 h/Mpc the amplitude of the correlated isocurvature component cannot be larger than about 60% for the cold dark matter mode, 40% for the neutrino density mode, and 30% for the neutrino velocity mode, at 2 sigma. In the first case, our bound is larger than the WMAP first-year result, presumably because we prefer not to include any data from Lyman-alpha forests, but then obtain large blue spectral indexes for the non-adiabatic contributions. We also translate our bounds in terms of constraints on double inflation models with two uncoupled massive fields., Comment: 12 pages, 5 figures

Braneworld scenarios with compact extra-dimensions need the volume of the extra space to be stabilized. Goldberger and Wise have introduced a simple mechanism, based on the presence of a bulk scalar field, able to stabilize the radius of the Randall-Sundrum model. Here, we transpose the same mechanism to generic single-brane and two-brane models, with one extra dimension and arbitrary scalar potentials in the bulk and on the branes. The single-brane construction turns out to be always unstable, independently of the bulk and brane potentials. In the case of two branes, we derive some generic criteria ensuring the stabilization or destabilization of the system., Comment: 8 pages, 2 figures. 1 figure and one subsection added. version published on PRD

Dwarf spiral galaxies - and in particular the prototypical DDO 154 - are known to be completely dominated by an unseen component. The putative neutralinos - so far the favored explanation for the astronomical dark matter - fail to reproduce the well measured rotation curves of those systems because these species tend to form a central cusp whose presence is not supported by observation. We have considered here a self-coupled charged scalar field as an alternative to neutralinos and investigated whether a Bose condensate of that field could account for the dark matter inside DDO 154 and more generally inside dwarf spirals. The size of the condensate turns out to be precisely determined by the scalar mass m and self-coupling lambda of the field. We find actually that for m^4 / lambda = 50 - 75 eV^4, the agreement with the measurements of the circular speed of DDO 154 is impressive whereas it lessens for larger systems. The cosmological behavior of the field is also found to be consistent - yet marginally - with the limits set by BBN on the effective number of neutrino families. We conclude that classical configurations of a scalar and self-coupled field provide a possible solution to the astronomical dark matter problem and we suggest further directions of research., Comment: 20 pages, 7 figures; one reference added, version to be published in PRD

A complex scalar field has recently been suggested to bind galaxies and flatten the rotation curves of spirals. Its cosmological behavior is thoroughly investigated here. Such a field is shown to be a potential candidate for the cosmological dark matter that fills up a fraction Omega_cdm = 0.3 of the Universe. However, problems arise when the limits from galactic dynamics and some cosmological constraints are taken simultaneously into account. A free complex field, associated to a very small mass m = 10^{-23} eV, has a correct cosmological behavior in the early Universe, but behaves today mostly as a real axion, with a problematic value of its conserved quantum number. On the other hand, an interacting field with quartic coupling lambda = 0.1 has a more realistic mass m = 1 eV and carries a quantum number close to the photon number density. Unlike a free field, it would be spinning today in the complex plane - like the so-called ``spintessence''. Unfortunately, the cosmological evolution of such field in the early Universe is hardly compatible with constraints from nucleosynthesis and structure formation., Comment: 13 pages, 3 figures. Some minor changes, version accepted in PRD

The nature of the dark matter that binds galaxies remains an open question. The favored candidate has been so far the neutralino. This massive species with evanescent interactions is now in difficulty. It would actually collapse in dense clumps and would therefore play havoc with the matter it is supposed to shepherd. We focus here on a massive and non-interacting charged scalar field as an alternate option to the astronomical missing mass. We investigate the classical solutions that describe the Bose condensate of such a field in gravitational interaction with matter. This simplistic model accounts quite well for the dark matter inside low-luminosity spirals whereas the agreement lessens for the brightest objects where baryons dominate. A scalar mass m=0.4 to 1.6 10^{-23} eV is derived when both high and low-luminosity spirals are fitted at the same time. Comparison with astronomical observations is made quantitative through a chi-squared analysis. We conclude that scalar fields offer a promising direction worth being explored., Comment: 16 pages, 5 figures

We provide the first complete analysis of cosmological evolution in the Randall-Sundrum model with stabilized dilaton. We give the exact expansion law for matter densities on the two branes with arbitrary equations of state. The effective four-dimensional theory leads to standard cosmology at low energy. The limit of validity of the low energy theory and possible deviations from the ordinary expansion law in the high energy regime are finally discussed., Comment: 16 pages

The behaviour of quantum metric perturbations produced during inflation is considered at the stage after the second Hubble radius crossing. It is shown that the classical correlation between amplitude and momentum of a perturbation mode, previously shown to emerge in the course of an effective quantum-to-classical transition, is maintained for a sufficiently long time, and we present the explicit form in which it takes place using the Wigner function. We further show with a simple diffraction experiment that quantum interference, non-expressible in terms of a classical stochastic description of the perturbations, is essentially suppressed. Rescattering of the perturbations leads to a comparatively slow decay of this correlation and to a complete stochastization of the system., Comment: LaTeX (7 pages)

We show how to determine the typical phase space volume $\Gamma$ for primordial gravitational waves produced during an inflationary stage, which is invariant under squeezing. An expression for $\Gamma$ is found in the long wavelength regime. The quasi-classical entropy of a pure vacuum initial state defined as the logarithm of $\Gamma$ modulo a constant remains zero in spite of the generation of fluctuations (creation of real gravitons)., Comment: LaTeX (10 pages)

Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger representations, as well as using the Wigner function. We show explicitly that these three approaches lead to the same prediction in the limit of large squeezing (i.e. when the squeezing parameter $|r_k|\to \infty$): each two-modes quantum state (k, -k) of these perturbations is equivalent to a classical perturbation that has a stochastic amplitude, obeying a non-gaussian statistics which depends on the initial state, and that belongs to the quasi-isotropic mode (i.e. it possesses a fixed phase). The Wigner function is not everywhere positive for any finite $r_k$, hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure. However, this does not affect the transition to semiclassical behaviour since the Wigner function becomes concentrated near a classical trajectory in phase space when $|r_k|\to \infty$ even without coarse graining. Deviations of the statistics of the perturbations in real space from a Gaussian one lie below the cosmic variance level for the N-particles initial states with N=N(|k|) but may be observable for other initial states without statistical isotropy or with correlations between different k modes. As a way to look for this effect, it is proposed to measure the kurtosis of the angular fluctuations of the cosmic microwave background temperature., Comment: LaTeX (28 pages),+2 eps figures