Logarithmic Extensions to Inflation Universality Classes

TL;DR

This paper explores logarithmic corrections to inflation universality classes, revealing how these modifications impact the tensor-to-scalar ratio and the detectability of certain inflation models, with implications for cosmological observations.

Contribution

It introduces a logarithmic N correction to inflation universality classes, analyzing its effects on the tilt and tensor-to-scalar ratio, and discusses implications for inflation model viability.

Findings

Logarithmic corrections can lower r in some models but are canceled out.

Near Starobinsky inflation, r can be increased, aiding detection.

The correction impacts the interpretation of inflation observables.

Abstract

The values of, and connection between, the cosmological observables of the primordial power spectrum tilt $n_s$ and the inflationary tensor to scalar ratio $r$ are key guideposts to the physics of inflation. Universality classes can be defined for the tilt from the scale free value proportional to $1/N$, where $N$ is the number of e-folds. We examine the consequences of a $\ln N$ next to leading order correction rather than an expansion in $1/N$, or introducing a new parameter. While nominally this can lower $r$ for some too-high $r$ simple inflation models (e.g. large field models), there is an interesting cancellation preventing such models from coming back into favor. On the other branch of the universality class, near Starobinsky inflation, $r$ can be raised, making it easier to detect.