Multiple Inflationary Stages with Varying Equation of State

TL;DR

This paper explores a model of inflation with multiple stages separated by different equations of state, leading to distinctive features in the curvature power spectrum that could impact CMB observations and black hole formation.

Contribution

It introduces a phenomenological inflation model with instantaneous transitions between different equations of state, revealing unique spectral modulations.

Findings

Power spectrum exhibits sinusoidal modulations due to phase transitions.

Different intermediate states (radiation, matter, kinetic) affect the spectral features.

Potential observational signatures in CMB and primordial black holes.

Abstract

We consider a model of inflation consisting a single fluid with a time-dependent equation of state. In this phenomenological picture, two periods of inflation are separated by an intermediate non-inflationary stage which can be either a radiation dominated, matter dominated or kinetic energy dominated universe, respectively, with the equation of state $w=1/3$, 0 or 1. We consider the toy model in which the change in $w$ happens instantaneously. Depending on whether the mode of interest leaves the horizon before or after or between the phase transitions, the curvature power spectrum can have non-trivial sinusoidal modulations. This can have interesting observational implications for CMB anisotropies and for primordial black-hole formation.