Back-reaction of Cosmological Fluctuations during Power-Law Inflation

TL;DR

This paper investigates how scalar fluctuations during power-law inflation influence the universe's expansion, revealing a negative energy density contribution and analyzing the behavior of inflaton fluctuations and adiabatic expansion.

Contribution

It provides a detailed analysis of the back-reaction effects of cosmological fluctuations during power-law inflation, including the energy-momentum tensor and inflaton fluctuation dynamics.

Findings

Back-reaction leads to decreased expansion rate.

Energy density of fluctuations is negative and scales with background.

Inflaton fluctuations are decoupled and follow the same equations.

Abstract

We study the renormalized energy-momentum tensor of cosmological scalar fluctuations during the slow-rollover regime for power-law inflation and find that it is characterized by a negative energy density at the leading order, with the same time behaviour as the background energy. The average expansion rate appears decreased by the back-reaction of the effective energy of cosmological fluctuations, but this value is comparable with the energy of background only if inflation starts at a Planckian energy. We also find that, for this particular model, the first and second order inflaton fluctuations are decoupled and satisfy the same equation of motion. To conclude, the fourth order adiabatic expansion for the inflaton scalar field is evaluated for a general potential V(\phi).