Inflation, Renormalization, and CMB Anisotropies

TL;DR

This paper demonstrates that quantum field renormalization in inflationary models alters the predicted relationship between tensor-to-scalar ratio and spectral indices, impacting observable CMB anisotropies.

Contribution

It introduces a novel renormalization approach that modifies the inflationary consistency condition, allowing for a non-zero tensor-to-scalar ratio with a scale-invariant tensor spectrum.

Findings

Renormalization changes the tensor-scalar consistency relation.

Scale-invariant tensor spectrum can coexist with non-zero r.

Predictions are testable with upcoming CMB observations.

Abstract

In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.