Universal Correction to the Inflationary Vacuum

TL;DR

This paper derives a fundamental correction to the inflationary vacuum state in de Sitter space, ensuring energy conservation and revealing a small but significant modification to the primordial power spectrum.

Contribution

It introduces a universal correction to the Bunch-Davies state based on energy conservation, altering the inflationary perturbation spectrum.

Findings

The correction replaces the Boltzmann factor with an entropy-based factor.

The modified state results in an ${ m O}(H/M_p)^2$ change to the primordial power spectrum.

The correction is explicitly calculable and physically motivated by energy conservation.

Abstract

The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor $\exp(-\beta \omega_k)$ replaced by $\exp(\Delta S)$, where $S$ is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine.