Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

TL;DR

This paper proposes a method for regularizing relic gravitational wave spectra that avoids low-frequency distortions by focusing on short modes during inflation, resulting in UV convergent spectra with potential observable oscillations.

Contribution

It introduces a selective regularization approach for relic gravitational waves that preserves low-frequency features and maintains energy conservation during inflation.

Findings

Spectra are UV convergent and free of low-frequency distortion.

Oscillations in the spectra are caused by mode interference and may be detectable.

Regularization at inflation, not present time, preserves spectral features.

Abstract

Adiabatic regularization is a method to remove UV divergences in quantum fields in curved spacetime. For relic gravitational wave generated during inflation, regularization on all $k$-modes of the power spectrum to 2nd adiabatic order, and of the energy density and pressure to 4th order, respectively, causes low-frequency distortions. To avoid these, we regularize only the short modes inside the horizon during inflation (corresponding to the present frequencies $f \gtrsim 10^{9}$Hz), and keep the long modes intact. Doing this does not violate the energy conservation since the $k$-modes of RGW are independent of each other during inflation. The resulting spectra are UV convergent and simultaneously free of low-frequency distortion, and these properties remain in the present spectra after evolution, in contrast to regularization at the present time which has some distortion or irregularities. The spectra generally exhibit quick oscillations in frequency domain, even if the initial spectra during inflation have no oscillations. This pattern is due to the interference between the positive and negative frequency modes developed during cosmic expansion, and may be probed by future RGW detections.