Decaying vacuum and evolution from early inflation to late acceleration

TL;DR

This paper explores decaying vacuum models where vacuum energy density evolves over time, providing a unified framework for the universe's history from early inflation to late acceleration, including solutions for primordial perturbations.

Contribution

It introduces a general solution to the Friedmann equation with a time-dependent vacuum energy density and defines an epoch-invariant mode number for perturbations crossing the Hubble radius.

Findings

Asymptotic solutions for different epochs derived

Finite boundaries for de Sitter epochs established

Number of perturbation modes crossing Hubble radius calculated

Abstract

Decaying vacuum models are a class of models that incorporate the vacuum energy density as a time-evolving entity that has the potential to explain the entire evolutionary history of the universe in a single framework. A general solution to the Friedmann equation can be obtained by considering vacuum energy density as a function of the Hubble parameter. We have obtained the asymptotic solution by choosing the appropriate equation of state for matter and radiation. Finite boundaries in the early and late de Sitter epoch could be defined by considering the evolution of primordial perturbation wavelength. An epoch invariant number $N_c$ determines the number of perturbation modes that cross the Hubble radii during each epoch has been obtained.