Universal Correction to the Inflationary Vacuum
Brian Greene, Maulik Parikh, Jan Pieter van der Schaar

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 replaced by , where 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 modification of the primordial power spectrum of inflationary perturbations, which we determine.
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