Inflationary dynamics and observables: β-exponential models in Palatini R2 gravity

Abstract

We focus on the inflationary predictions of β-exponential potential models, in which the inflaton is associated with a field that determines the size of extra dimensions. This provides a well-motivated starting point for exploring physics at very high energy scales. Consequently, we incorporate an $R^2$ term within the Palatini formulation of gravity. Additionally, we extend our analysis by examining the effects of reheating on inflationary observables, considering various scenarios for the reheat temperature. We present the inflationary predictions for spectral index $n_s$, tensor-to-scalar ratio r, and the running of the spectral index $d{n}_s/d\ln k$ in the context of a β-exponential potential minimally coupled in Palatini $R^2$ gravity. Furthermore, we confront our results with observational constraints from BICEP/Keck, Planck 2018, and the most recent Planck+ACT DR6 data released by the ACT collaboration. We also consider the projected sensitivities of upcoming CMB experiments, including CMB-S4, LiteBIRD, and SPIDER. Our findings demonstrate the viability of the model, even in light of the tighter constraints expected from future data.