Inverse Symmetric Inflationary Attractors

TL;DR

This paper introduces inverse symmetric inflationary potentials, explores their similarities and differences with $ ext{alpha}$-attractors and Starobinsky models, and examines their viability and connections to $F(R)$ gravity and non-minimal coupling.

Contribution

It presents a new class of inverse symmetric inflationary potentials, analyzes their observational viability, and links them to $F(R)$ gravity and non-minimal coupling theories.

Findings

Inverse symmetric models can match observational data depending on their asymptotic form.

When matching $ ext{alpha}$-attractors, compatibility with observations is guaranteed.

The $F(R)$ gravity equivalent belongs to the $R^2$ attractor class.

Abstract

We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreover, we study the corresponding $F(R)$ gravity theory and we show that the Jordan frame theory belongs to the $R^2$ attractor class of models. Finally we discuss a non-minimally coupled theory and we show that the attractor behavior occurs in this case too.