Constant Roll Inflationary Dynamics with Generalized Potentials in $f(R,\varphi ,X)$ Gravity

Abstract

In this work, we study early-time inflation within a class of $f(R,\varphi ,X)$ gravity models under a constant-roll condition. Employing a generalized potential of the form $V(\varphi {)}^{\sigma }$, we derive expressions for the spectral index $n_s$ and tensor-to-scalar ratio $r$, demonstrating that the inflationary dynamics are primarily governed by the parameter $\sigma$ and the shape of the potential. At the upper limit of $n_s$, we obtain a de Sitter-like phase, while at the lower limit, the model transitions to a quintessence-like phase through an effective oscillating equation of state parameter (EoS). Therefore, under the tuning parameter $\sigma <1$, the model exhibits a smooth transition from a de Sitter-like phase to a quintessence-like phase via the oscillating EoS parameter. The resulting predictions are consistent with recent observations from the Atacama Cosmology Telescope (ACT), combined with CMB lensing and DESI BAO data.

arXiv commentPLB accepted

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