On vacuum density, the initial singularity and dark energy

TL;DR

This paper explores how vacuum energy influences the early and late accelerated phases of the universe, analyzing scalar field models and primordial perturbations, revealing the necessity of inflation and a harmonic potential at late times.

Contribution

It models vacuum energy effects in cosmology using scalar fields, connecting early universe inflation and late-time acceleration with novel potential forms.

Findings

Early spectrum not scale-invariant, requiring inflation

Late-time potential is harmonic with Hubble-scale mass

Vacuum energy models can be non-singular and inflationary

Abstract

Standard cosmology poses a number of important questions. Apart from its singular origin, it possesses early and late accelerating phases required to account for observations. The vacuum energy has been considered as a possible way to resolve some of these questions. The vacuum energy density induced by free fields in an early de Sitter phase has earlier been estimated to be proportional to $H^4$, while more recently it has been suggested that the QCD condensate induces a term proportional to H at late times. These results have been employed in models which are non-singular and inflationary at early times and accelerating at late times. Here we cast these models in terms of scalar fields and study the corresponding spectrum of primordial perturbations. At early times the spectrum is found to be not scale-invariant, thus implying that slow-roll inflation is still required after the phase transition induced by the vacuum. At late times the corresponding scalar-field potential is harmonic, with a mass of the order of the Hubble scale, a result that may be understood in the light of the holographic conjecture.