Modeling Cosmological Perturbations of Thermal Inflation

TL;DR

This paper models how thermal inflation affects primordial perturbations, revealing characteristic transfer functions influenced by vacuum energy and phase changes, which could impact observable cosmological signatures.

Contribution

It introduces a simple matter-radiation-vacuum model to derive the transfer function of primordial perturbations during thermal inflation, highlighting the dependence on vacuum energy ratio and characteristic scales.

Findings

Transfer function shape depends on vacuum energy ratio $
$.

Distinct oscillation patterns emerge for different $
$ regimes.

Characteristic scales $k_a$ and $k_b$ determine the transfer function features.

Abstract

We consider a simple system consisting of matter, radiation and vacuum components to model the impact of thermal inflation on the evolution of primordial perturbations. The vacuum energy magnifies the primordial modes entering the horizon before its domination, making them potentially observable, and the resulting transfer function reflects the phase changes and energy contents. To determine the transfer function, we follow the curvature perturbation from well outside the horizon during radiation domination to well outside the horizon during vacuum domination and evaluate it on a constant radiation density hypersurface, as is appropriate for the case of thermal inflation. The shape of the transfer function is determined by the ratio of vacuum energy to radiation at matter-radiation equality, which we denote by $\upsilon$, and has two characteristic scales, $k_{\rm a}$ and $k_{\rm b}$, corresponding to the horizon sizes at matter radiation equality and the beginning of the inflation, respectively. If $\upsilon \ll 1$, the universe experiences radiation, matter and vacuum domination eras and the transfer function is flat for $k \ll k_{\rm b}$, oscillates with amplitude $1/5$ for $ k_{\rm b} \ll k \ll k_{\rm a}$ and oscillates with amplitude $1$ for $k \gg k_{\rm a}$. For $\upsilon \gg 1$, the matter domination era disappears, and the transfer function reduces to being flat for $k \ll k_{\rm b}$ and oscillating with amplitude $1$ for $k \gg k_{\rm b}$.