On the Problem of Vacuum Energy in FLRW Universes and Dark Energy

TL;DR

This paper presents a novel quantum field theory calculation of vacuum energy in expanding FLRW universes, showing that the leading correction aligns with the observed dark energy density, thus offering insights into the cosmological constant problem.

Contribution

It introduces a new method for calculating vacuum energy in cosmological backgrounds using renormalization, connecting quantum field theory with dark energy observations.

Findings

Leading correction to vacuum energy scales as H_0^2 * Lambda_pl

Correction magnitude matches observed dark energy density

Provides a quantum field theoretical approach to vacuum energy in cosmology

Abstract

We present a (hopefully) novel calculation of the vacuum energy in expanding FLRW spacetimes based on the renormalization of quantum field theory in non-zero backgrounds. We compute the renormalized effective action up to the $2-$point function and then apply the formalism to the cosmological backgrounds of interest. As an example we calculate for quasi de Sitter spacetimes the leading correction to the vacuum energy given by the tadpole diagram and show that it behaves as $\sim H_0^2 \Lambda_{\rm pl}$ where $H_0$ is the Hubble constant and $\Lambda_{\rm pl}$ is the Planck constant. This is of the same order of magnitude as the observed dark energy density in the universe.