Exact Perturbations for inflation with smooth exit

TL;DR

This paper presents exact solutions for scalar and tensor perturbations during a smooth transition from inflation to radiation era, using a Hubble rate from decaying vacuum cosmology, confirming conserved quantities for super-horizon modes.

Contribution

It introduces a consistent Hubble rate from decaying vacuum cosmology and derives exact solutions for perturbations during inflation to radiation transition.

Findings

Super-horizon scalar perturbations are exactly conserved for growing modes.

Exact solutions for sub-horizon perturbations in vacuum and radiation eras.

Super-horizon decaying modes are exactly zero.

Abstract

Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently from a decaying vacuum cosmology, which evolves smoothly from nearly de Sitter inflation to radiation domination. We find exact solutions for super-horizon perturbations (scalar and tensor), and for sub-horizon perturbations in the vacuum- and radiation-dominated eras. The standard conserved quantity for super-horizon scalar perturbations is exactly constant for growing modes, and zero for the decaying modes.