Second-Order Cosmological Perturbations from Inflation

TL;DR

This paper computes second-order cosmological perturbations during inflation, providing an exact gauge-invariant bispectrum expression that characterizes non-Gaussian features, but suggests detection will be challenging.

Contribution

It presents the first detailed second-order calculation of inflationary perturbations, including self-interactions and metric fluctuations, with explicit bispectrum expressions.

Findings

Provides the exact gauge-invariant bispectrum during inflation.

Shows non-Gaussianity from second-order effects is difficult to detect.

Connects bispectrum to slow-roll parameters, $n_S$, and $r$.

Abstract

We present the first computation of the cosmological perturbations generated during inflation up to second order in deviations from the homogeneous background solution. Our results, which fully account for the inflaton self-interactions as well as for the second-order fluctuations of the background metric, provide the exact expression for the gauge-invariant curvature perturbation bispectrum produced during inflation in terms of the slow-roll parameters or, alternatively, in terms of the scalar spectral $n_S$ and and the tensor to adiabatic scalar amplitude ratio $r$. The bispectrum represents a specific non-Gaussian signature of fluctuations generated by quantum oscillations during slow-roll inflation. However, our findings indicate that detecting the non-Gaussianity in the cosmic microwave background anisotropies emerging from the second-order calculation will be a challenge for the forthcoming satellite experiments.