Constant-roll $\beta$-exponential inflation: Palatini formalism

TL;DR

This paper investigates a scalar field model with a $eta$-exponential potential within the Palatini formalism, analyzing its inflationary predictions under constant-roll conditions and comparing results with recent cosmological observations.

Contribution

It introduces a novel inflationary model coupling a scalar field to quadratic gravity in the Palatini formalism and analyzes its observational viability under constant-roll assumptions.

Findings

Model predictions align with ACT DR6 and Planck data.

Identifies parameter space consistent with current cosmological observations.

Provides a new framework for inflation with extra-dimensional implications.

Abstract

In this paper, we explore the inflationary dynamics of the $\beta$-exponential potential model, where a scalar field couples to quadratic $(R + R^2)$ gravity. In this model, the inflaton is the field that determines the size of the extra dimension. We employ the Palatini formalism to derive the resulting Einstein-frame generalized $k$-inflation effective theory, which we analyze under the assumption that the constant-roll condition is satisfied. We scan the parameter space for inflationary predictions, specifically the spectral index $n_s$ and the tensor-to-scalar ratio $r$, ensuring consistency with the results from ACT DR6. The compliant regions are depicted accordingly. For a suitable range of the model parameters, the values obtained for the inflationary observables align with the most recent observations by the Atacama Cosmology Telescope (ACT) collaboration and/or the Planck mission.