$\tilde\xi$-attractors in metric-affine gravity

TL;DR

This paper introduces a new class of inflationary models called $ ilde\xi$-attractors in metric-affine gravity, which unify features of $ ilde\cal R^2$ models and Starobinsky inflation through strong coupling limits.

Contribution

It proposes a novel class of inflationary attractors involving non-minimal coupling with the Holst invariant and explores their behavior in strong coupling regimes.

Findings

At large $ ilde\xi$, the model reduces to a $ ilde\cal R^2$ theory.

Small Barbero-Immirzi parameter aligns predictions with Starobinsky inflation.

The class exhibits attractor behavior similar to $\xi$-attractors.

Abstract

We propose a new class of inflationary attractors in metric-affine gravity. Such class features a non-minimal coupling $\tilde\xi \, \Omega(\phi)$ with the Holst invariant $\tilde{\cal R}$ and an inflaton potential proportional to $\Omega(\phi)^2$. The attractor behaviour of the class takes place with two combined strong coupling limits. The first limit is realized at large $\tilde\xi$, which makes the theory equivalent to a $\tilde{\cal R}^2$ model. Then, the second limit considers a very small Barbero-Immirzi parameter which leads the inflationary predictions of the $\tilde{\cal R}^2$ model towards the ones of Starobinsky inflation. Because of the analogy with the renown $\xi$-attractors, we label this new class as $\tilde\xi$-attractors.