Reheating, multifield inflation and the fate of the primordial observables

Godfrey Leung,Christian T Byrnes,Edmund J Copeland,Ewan R.M Tarrant

doi:10.1088/1475-7516/2012/09/008

Abstract

We study the effects of perturbative reheating on the evolution of the curvature perturbation ζ, in two-field inflation models. We use numerical methods to explore the sensitivity of fNL, nζ and r to the reheating process, and present simple qualitative arguments to explain our results.In general, if a large non-Gaussian signal exists at the start of reheating, it will remain non-zero at the end of reheating.Unless all isocurvature modes have completely decayed before the start of reheating, we find that the non-linearity parameter, fNL, can be sensitive to the reheating timescale, and that this dependence is most appreciable for `runaway' inflationary potentials that only have a minimum in one direction. For potentials with a minimum in both directions, fNL can also be sensitive to reheating if a mild hierarchy exists between the decay rates of each field.Within the class of models studied, we find that the spectral index nζ, is fairly insensitive to large changes in the field decay rates, indicating that nζ is a more robust inflationary observable, unlike the non-linearity parameter fNL.Our results imply that the statistics of ζ, especially fNL, can only be reliably used to discriminate between models of two-field inflation if the physics of reheating are properly accounted for.

Highlights

Inflation has become the dominant paradigm for explaining the generation of the primordial density perturbation ζ, that seeded structure formation, and the Cosmic Microwave Background (CMB) anisotropies
If a large non–Gaussian signal exists at the start of reheating, it will remain non–zero at the end of reheating
Within the class of models studied, we find that the spectral index nζ, is fairly insensitive to large changes in the field decay rates, indicating that nζ is a more robust inflationary observable, unlike the non–linearity parameter fNL

Summary

INTRODUCTION

Inflation has become the dominant paradigm for explaining the generation of the primordial density perturbation ζ, that seeded structure formation, and the Cosmic Microwave Background (CMB) anisotropies. This is partly motivated by the work of [38] where two broad classes of behaviour for the evolution of ζ were recognised: Potentials that contain a ‘natural focussing region’, which is guaranteed for a two–field model with minima in both directions, allow neighbouring trajectories in field space to converge ‘naturally’, quenching the flow of power from isocurvature modes to ζ No such focussing region may exist, which is the case for a two–field model with only a single minimum, and so ζ will continue to evolve until an adiabatic condition is reached. Predictions for observables such as fNL cannot currently be linked directly to the physics of the inflationary model, as they will be dependent on the subsequent phase of reheating Even in the former case, if the universe approaches adiabaticity by the inflating/isocurvature trajectories converging in, and oscillating about, their global minima, it is not clear how the decay of the oscillating fields into radiation affects the final stages of the evolution of ζ. In the following subsections we introduce the simple perturbative reheating scheme that we use throughout this paper, and briefly review the δN formalism that is used to compute the statistics of ζ

Elementary theory of reheating

The δN Formalism and non–Gaussianity

Numerical Code

ONE MINIMUM

Spectral index and tensor–to–scalar ratio

TWO MINIMA

Quadratic minimum

Quartic minimum

NON-SEPARABLE POTENTIAL WITH ONE MINIMUM

DISCUSSION AND CONCLUSIONS