Revising the observable consequences of slow-roll inflation

TL;DR

This paper explores how proper renormalization in slow-roll inflation modifies the predicted primordial power spectra and the relation between tensor-to-scalar ratio and spectral indices, impacting observable CMB signatures.

Contribution

It introduces a unique renormalization approach in an expanding universe that alters inflationary predictions for primordial perturbations and their observable consequences.

Findings

Altered scalar and tensor power spectra predictions.

Modified consistency relation between r and spectral indices.

Scale-invariant tensor spectrum now compatible with non-zero r.

Abstract

We study the generation of primordial perturbations in a (single-field) slow-roll inflationary universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a non-zero variance $\Delta^2(k, t)$. However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize $\Delta^2(k, t)$. This can (and should) be achieved by proper renormalization in an expanding universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the CMB anisotropies is significantly altered. 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 $r\approx 0.12\pm0.06$, which is forbidden by the standard prediction ($r=-8n_t$). The influence of relic gravitational waves on the CMB may soon come within the range of planned measurements, offering a non-trivial test of the new predictions.