Late time acceleration in Palatini gravity

TL;DR

This paper studies how quadratic and non-minimal coupling corrections in Palatini gravity affect quintessence models with exponential potential, revealing that non-minimal coupling can drive late-time acceleration while quadratic correction is mostly relevant at early times.

Contribution

It demonstrates that non-minimal coupling can produce viable late-time acceleration in Palatini gravity, while quadratic correction has limited impact on late-time dynamics.

Findings

Quadratic correction $ ightarrow$ negligible in late-time dynamics unless very large.

Non-minimal coupling $ ightarrow$ can drive late-time accelerated expansion.

Field ends up frozen, mimicking a cosmological constant.

Abstract

We investigate the effect of the quadratic correction $\alpha R^2$ and non-minimal coupling $\xi \phi^2 R$ on a quintessence model with an exponential potential $V(\phi) = M^4\exp(-\lambda\phi)$ in the Palatini formulation of gravity. We use dynamical system techniques to analyze the attractor structure of the model and uncover the possible trajectories of the system. We find that the quadratic correction cannot play a role in the late time dynamics, except for unacceptably large values of the parameter $\alpha$; although it can play a role at early times. We find viable evolutions, from a matter-dominated phase to an accelerated expansion phase, with the dynamics driven by the non-minimal coupling. These evolutions correspond to trajectories where the field ends up frozen, thus acting as a cosmological constant.