Palatini $F(R,X)$: a new framework for inflationary attractors

TL;DR

This paper introduces a new $F(R+X)$ gravity framework that addresses issues in inflationary models by generating fractional attractors, expanding the landscape of inflationary solutions beyond traditional polynomial attractors.

Contribution

It proposes a novel $F(R+X)$ gravity model that naturally produces fractional attractors, generalizing the polynomial $eta$-attractors and improving inflationary dynamics.

Findings

$F(R+X)$ gravity resolves slow-roll issues in inflation.

Quadratic $F$ leads to fractional attractors.

New class of inflationary attractors generalizing $eta$-attractors.

Abstract

Palatini $F(R)$ gravity proved to be a powerful tool in order to realize asymptotically flat inflaton potentials. Unfortunately, it also inevitably implies higher-order inflaton kinetic terms in the Einstein frame that might jeopardize the evolution of the system out of the slow-roll regime. We prove that a $F(R+X)$ gravity, where $X$ is the inflaton kinetic term, solves the issue. Moreover, when $F$ is a quadratic function such a choice easily leads to a new class of inflationary attractors, fractional attractors, that generalizes the already well-known polynomial $\alpha$-attractors.