Universal Correction to the Inflationary Vacuum

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 $\mathcal{O}(H/M_p{)}^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine.

23 pages, 3 eps figures, uses JHEP.cls, small corrections and added references

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