Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes

Abstract

We reexamine the regularization of the two-point function of a scalar field in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic regularization provides a set of subtraction terms in momentum space that successfully remove its ultraviolet divergences at coincident points, but can significantly distort the power spectrum at infrared scales, especially for light fields. In this work we propose, by using the intrinsic ambiguities of the renormalization program, a new set of subtraction terms that minimize the distortions for scales $k\lesssim M$, with $M$ an arbitrary mass scale. Our method is consistent with local covariance and equivalent to general regularization methods in curved spacetime. We apply our results to the regularization of the power spectrum in de Sitter space: while the adiabatic scheme yields exactly ${\Delta }_{\varphi }^{(\mathrm{reg})}=0$ for a massless field, our proposed prescription recovers the standard scale-invariant result ${\Delta }_{\varphi }^{(\mathrm{reg})}\simeq H^2/(4{\pi }^2)$ at super-horizon scales.

Title changed with respect to first version. New section added on renormalization conditions and coupling constants (Sect. 3). It matches the published version in PLB. 6 pages + references, 1 figure

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• Perturbative Quantum Gravity Comes of Age
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Cited by in corpus (3)

• Large fluctuations in the Sky
• An Étude on the Regularization and Renormalization of Divergences in Primordial Observables
• Physical scale adiabatic regularization in cosmological spacetimes