Non-linear inflationary perturbations

Abstract

We present a method by which cosmological perturbations can be quantitatively studied in single and multi-field inflationary models beyond linear perturbation theory. A non-linear generalization of the gauge-invariant Sasaki-Mukhanov variables is used in a long-wavelength approximation. These generalized variables remain invariant under time slicing changes on long wavelengths. The equations they obey are relatively simple and can be formulated for a number of time slicing choices. Initial conditions are set after horizon crossing and the subsequent evolution is fully non-linear. We briefly discuss how these methods can be implemented numerically to the study of non-Gaussian signatures from specific inflationary models.

One-loop corrections to scalar and tensor perturbations during inflation in stochastic gravity

“…To consider the origin of this logarithmic corrections due to the IR cut-off, we first mention the prediction in stochastic inflation [40][41][42][44][45][46][47][48][49][50][51]. In stochastic inflation, the long wave mode k with k < aH of the scalar field couples to the short wave mode k with k > aH through the nonlinear selfinteraction of the scalar field.…”

Primordial non-Gaussianities of general multiple-field inflation

“…A common choice is the non-linearity parameter f NL defined as 33) which denotes the departure of ζ from a Gaussian random variable ζ g . The power spectrum and bispectrum of ζ are defined in terms of the two and three-point functions respectively as…”

“…Indeed, in models descending from the low-energy limit of superstring theory or string compactification, there are many light moduli fields describing the higher-dimensional degrees of freedom, which could play a role during inflation. Therefore, it is interesting and of physical significance to generalize the above analysis of non-Gaussianities in single-field models to the multiple-field inflation models [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]. Most of the previous works focus on the models with standard canonical kinetic terms for the scalar fields involved.…”

Primordial non-Gaussianities from multiple-field inflation

“…In particular, deviations away from Gaussian statistics represent a potentially powerful discriminant between competing inflationary models and have attracted considerable recent interest [10,11,12,13,14,15,16,17,18,19]. Moreover, measurements of CMB anisotropies are now approaching a level of precision where such differences could soon be detectable and, indeed, the first non-gaussian signals in the data may already have been observed [20,21,22,23] (see also [24]).…”