Non-Gaussianity from Inflation: Theory and Observations

This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.Comment: LaTeX file: 218 pages, 19 figures. Replaced to match the accepted version in Physics Reports. A high-resolution version of Fig. 2 can be downloaded from: http://www.pd.infn.it/~liguori/Non_Gaussianity

CMB temperature anisotropies from third order gravitational perturbations

In this paper we present a complete computation of the Cosmic Microwave Background (CMB) anisotropies up to third order from gravitational perturbations accounting for scalar, vector and tensor perturbations. We then specify our results to the large scale limit, providing the evolution of the gravitational potentials in a flat universe filled with matter and cosmological constant which characterizes the Integrated Sachs-Wolfe effect. As a byproduct in the large scale approximation we are able to give non-perturbative solutions for the photon geodesic equations. Our results are the first step to provide a complete theoretical prediction for cubic non-linearities which are particularly relevant for characterizing the level of non-Gaussianity in the CMB through the detection of the four-point angular connected correlation function (trispectrum). For this purpose we also allow for generic initial conditions due to primordial non-Gaussianity.Comment: 19 pages, LateX file; typos corrected; some corrections made and several consistency checks performed regarding Eqs.(2.18); (2.28)-(2.29) and Eqs.(3.8)-(3.24) and Eq.(4.2). Version accepted for publication in JCA

Second-order matter perturbations in a LambdaCDM cosmology and non-Gaussianity

We obtain exact expressions for the effect of primordial non-Gaussianity on the matter density perturbation up to second order in a LambdaCDM cosmology, fully accounting for the general relativistic corrections arising on scales comparable with the Hubble radius. We present our results both in the Poisson gauge and in the comoving and synchronous gauge, which are relevant for comparison to different cosmological observables.Comment: 15 pages. LaTeX file. Invited article for CQG issue on non-linear cosmolog

Non-Gaussianity of Large-Scale Cosmic Microwave Background Anisotropies beyond Perturbation Theory

We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the n-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- and four-point connected correlation functions whose detection in future CMB experiments might be used to assess the level of primordial non-Gaussianity, giving the theoretical predictions for the parameters of quadratic and cubic non-linearities f_NL and g_NL.Comment: 24 pages, LaTeX file; Revised to match the final version accepted for publication on JCAP (some comments added in Sec.II and V

CMB Anisotropies at Second Order I

We present the computation of the full system of Boltzmann equations at second-order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow to follow the time evolution of the Cosmic Microwave Background (CMB) anisotropies at second-order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is so relevant for the issue of non-Gaussianity in the CMB anisotropies.Comment: 26 pages, LaTeX file, typos correcte

The Maximal Amount of Gravitational Waves in the Curvaton Scenario

The curvaton scenario for the generation of the cosmological curvature perturbation on large scales represents an alternative to the standard slow-roll scenario of inflation in which the observed density perturbations are due to fluctuations of the inflaton field itself. Its basic assumption is that the initial curvature perturbation due to the inflaton field is negligible. This is attained by lowering the energy scale of inflation, thereby highly suppressing the amount of gravitational waves produced during inflation. We compute the power-spectrum of the gravitational waves generated at second order in perturbation theory by the curvaton (isocurvature) perturbations between the end of inflation and the curvaton decay. An interesting property of this contribution to the tensor perturbations is that it is directly proportional to the amount of non-Gaussianity predicted within the curvaton scenario. We show that the spectrum of gravitational waves may be in the range of future gravitational wave detectors.Comment: 4 pages, laTeX; added a clarifying comment in the conclusions, version matches publication in PRD, Rapid Communication

The Full Second-Order Radiation Transfer Function for Large-Scale CMB Anisotropies

We calculate the full second-order radiation transfer function for Cosmic Microwave Background anisotropies on large angular scales in a flat universe filled with matter and cosmological constant. It includes (i) the second-order generalization of the Sachs-Wolfe effect, and of (ii) both the early and late Integrated Sachs-Wolfe effects, (iii) the contribution of the second-order tensor modes, and is valid for a generic set of initial conditions specifying the level of primordial non-Gaussianity.Comment: 30 pages, LaTeX fil

Signatures of Primordial Non-Gaussianity in the Large-Scale Structure of the Universe

We discuss how primordial (e.g. inflationary) non-Gaussianity in the cosmological perturbations is left imprinted in the Large-Scale Structure of the universe. Our findings show that the information on the primordial non-Gaussianity set on super-Hubble scales flows into Post-Newtonian terms, leaving an observable imprint in the Large-Scale Structure. Future high-precision measurements of the statistics of the dark matter density and peculiar velocity fields will allow to pin down the primordial non-Gaussianity, thus representing a tool complementary to studies of the Cosmic Microwave Background anisotropies.Comment: 8 pages, LaTeX file; Revised to match the final version accepted for publication on JCAP (some comments and one figure added

Characterizing the cosmological gravitational wave background: Anisotropies and non-Gaussianity

A future detection of the stochastic gravitational wave background (SGWB) with gravitational wave (GW) experiments is expected to open a new window on early universe cosmology and on the astrophysics of compact objects. In this paper we study SGWB anisotropies, that can offer new tools to discriminate between different sources of GWs. In particular, the cosmological SGWB inherits its anisotropies both (i) at its production and (ii) during its propagation through our perturbed universe. Concerning (i), we show that it typically leads to anisotropies with order one dependence on frequency. We then compute the effect of (ii) through a Boltzmann approach, including contributions of both large-scale scalar and tensor linearized perturbations. We also compute for the first time the three-point function of the SGWB energy density, which can allow one to extract information on GW non-Gaussianity with interferometers. Finally, we include nonlinear effects associated with long wavelength scalar fluctuations, and compute the squeezed limit of the 3-point function for the SGWB density contrast. Such limit satisfies a consistency relation, conceptually similar to that found in the literature for the case of cosmic microwave background perturbations

Anisotropies and non-Gaussianity of the cosmological gravitational wave background

The stochastic gravitational wave background (SGWB) is expected to be a key observable for gravitational wave (GW) interferometry. Its detection will open a new window to early Universe cosmology and to the astrophysics of compact objects. Using a Boltzmann approach, we study the angular anisotropies of the GW energy density, which is an important tool to disentangle the different cosmological and astrophysical contributions to the SGWB. Anisotropies in the cosmological background are imprinted both at its production and by GW propagation through the large-scale scalar and tensor perturbations of the Universe. The first contribution is not present in the cosmic microwave background radiation (as the Universe is not transparent to photons before recombination), causing an order 1 dependence of the anisotropies on frequency. Moreover, we provide a new method to characterize the cosmological SGWB through its possible deviation from Gaussian statistics. In particular, the SGWB will become a new probe of the primordial non-Gaussianity of the large-scale cosmological perturbations