Inflationary quasi-scale invariant attractors

TL;DR

This paper introduces a class of non-analytic inflationary potentials in the Einstein frame, linked to quasi-scale invariant models in the Jordan frame, which fit observational data and differ from traditional $oldsymbol{ extalpha}$-attractors.

Contribution

It identifies non-analytic potentials in the Einstein frame corresponding to quasi-scale invariant models in the Jordan frame, expanding the landscape of inflationary models compatible with observations.

Findings

Derived the functional form of non-analytic potentials consistent with quasi-scale invariance.

Established a universal relation between $r$ and $n_s$ distinct from $ extalpha$-attractors.

Linked classical scale invariance breaking to one-loop quantum corrections.

Abstract

In a series of recent papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $\alpha$. These so-called $\alpha$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $\alpha$-attractors is a non-canonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a non-canonical scalar kinetic energy, we explore the case of non-analytic potentials. We find the functional form that corresponds to quasi-scale invariant gravitational models in the Jordan frame, characterised by a universal relation between $r$ and $n_{s}$ that fits the observational data but is clearly distinct from the one of the $\alpha$-attractors. It is known that the breaking of the exact classical scale-invariance in the Jordan frame can be attributed to one-loop corrections. Therefore we conclude that there exists a class of non-analytic potentials in the non-canonical Einstein frame that are physically equivalent to a class of models in the Jordan frame, with scale-invariance softly broken by one-loop quantum corrections.