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

Abstract

We propose a new class of inflationary attractors in metric-affine gravity. Such class features a non-minimal coupling $\tilde{\xi }\Omega (\varphi )$ with the Holst invariant $\tilde{\mathcal{R}}$ and an inflaton potential proportional to $\Omega (\varphi {)}^2$. 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 ${\tilde{\mathcal{R}}}^2$ model. Then, the second limit considers a very small Barbero-Immirzi parameter which leads the inflationary predictions of the ${\tilde{\mathcal{R}}}^2$ 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.

Comments: v4, 18 pages, 3 figures, typos corrected in some equations, results unchanged, matches the erratum version