Inhomogeneous non-Gaussianity

We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher-order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.Comment: 16 pages, 2 figures; v2: Minor changes and references added. Matches the published versio

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

Local non-Gaussianity from inflation

The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.Comment: 21 pages, 1 figure, invited review to appear in Classical and Quantum Gravity special issue on non-linear and non-Gaussian cosmological perturbation

Local non-Gaussianity from rapidly varying sound speeds

We study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we consider a model of multiple-field DBI and use the deltaN formalism to track the super-horizon evolution of perturbations. By adopting a sum separable Hubble parameter we derive analytic expressions for the relevant quantities in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non-Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider two-field inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process.Comment: 30 pages, 7 figures; typos corrected, references added, accepted for publication in JCA

On the Physical Significance of Infra-red Corrections to Inflationary Observables

Inflationary observables, like the power spectrum, computed at one- and higher-order loop level seem to be plagued by large infra-red corrections. In this short note, we point out that these large infra-red corrections appear only in quantities which are not directly observable. This is in agreement with general expectations concerning infra-red effects.Comment: 11 pages; LateX file; 5 figures. Some coefficients in Eq.(A6) corrected; References adde

Classical approximation to quantum cosmological correlations

We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $\phi^3$ theory on a de Sitter background for a massless minimally coupled scalar field $\phi$. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references, conclusions unchanged; v3: added section in which we compare with stochastic approach; this version matches published versio

Multiple field inflation

Inflation offers a simple model for very early evolution of our Universe and the origin of primordial perturbations on large scales. Over the last 25 years we have become familiar with the predictions of single-field models, but inflation with more than one light scalar field can alter preconceptions about the inflationary dynamics and our predictions for the primordial perturbations. I will discuss how future observational data could distinguish between inflation driven by one field, or many fields. As an example, I briefly review the curvaton as an alternative to the inflaton scenario for the origin of structure.Comment: 27 pages, no figures. To appear in proceedings of 22nd IAP Colloquium, Inflation +25, Paris, June 200

Infrared effects in inflationary correlation functions

In this article, I briefly review the status of infrared effects which occur when using inflationary models to calculate initial conditions for a subsequent hot, dense plasma phase. Three types of divergence have been identified in the literature: secular, "time-dependent" logarithms, which grow with time spent outside the horizon; "box-cutoff" logarithms, which encode a dependence on the infrared cutoff when calculating in a finite-sized box; and "quantum" logarithms, which depend on the ratio of a scale characterizing new physics to the scale of whatever process is under consideration, and whose interpretation is the same as conventional field theory. I review the calculations in which these divergences appear, and discuss the methods which have been developed to deal with them.Comment: Invited review for focus section of Classical & Quantum Gravity on nonlinear and nongaussian perturbation theory. Some improvements compared to version which will appear in CQG, especially in Sec. 2.3. 30 pages + references

Strongly scale-dependent polyspectra from curvaton self-interactions

We study the scale dependence of the non-linearity parameters f_NL and g_NL in curvaton models with self-interactions. We show that the spectral indices n_fNL=d ln|f_NL|/(d ln k) and n_gNL=d ln |g_NL|/(d ln k) can take values much greater than the slow--roll parameters and the spectral index of the power spectrum. This means that the scale--dependence of the bi and trispectrum could be easily observable in this scenario with Planck, which would lead to tight additional constraints on the model. Inspite of the highly non-trivial behaviour of f_NL and g_NL in the curvaton models with self-interactions, we find that the model can be falsified if g_NL(k) is also observed.Comment: 19 pages, many figures. v2: Figure 4 replaced with a corrected normalisation, conclusions unchanged. Matches version published in JCA

One-loop corrections to a scalar field during inflation

The leading quantum correction to the power spectrum of a gravitationally-coupled light scalar field is calculated, assuming that it is generated during a phase of single-field, slow-roll inflation.Comment: 33 pages, uses feynmp.sty and ioplatex journal style. v2: matches version published in JCAP. v3: corrects sign error in Eq. (58). Corrects final coefficient of the logarithm in Eq. (105). Small corrections to discussion of divergences in 1-point function. Minor improvements to discussion of UV behaviour in Sec. 4.