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

TL;DR

The paper investigates early-universe inflation within a generalized gravity framework $f(R,φ,X)$ under a constant-roll condition, employing a generalized potential $V(φ)^{σ}$. By deriving the FRW dynamics and slow-roll parameters, it shows that the inflationary observables $n_s$ and $r$ are primarily governed by the exponent $σ$ and the potential shape, enabling a two-stage evolution: a de Sitter-like inflation at the upper $n_s$ bound and a subsequent quintessence-like phase as $σ$ increases. The generalized chaotic potential $V(φ)^{σ}$ yields $n_s$ and $r$ that depend on $(n,σ,δ)$, with observationally viable regions constrained by ACT, Planck, and BAO data; in particular, for $n=2$, $0.00199622 < σ < 0.6263$ and $0.9709 \,\leq\, n_s \,\leq\, 0.9777$. A key result is the oscillating EoS parameter $w_e = (nσ-2)/(nσ+2)$, which, together with $a ∝ φ^{σ/|ε_1|}$, mediates a σ-controlled transition from a quasi-de Sitter phase to a quintessence-like inflationary regime, connecting early-universe dynamics with theoretical expectations from UV-complete frameworks.

Abstract

In this work, we study early-time inflation within a class of $f(R, φ, X)$ gravity models under a constant-roll condition. Employing a generalized potential of the form $V(φ)^σ$, 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 $σ$ 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 $σ< 1$, 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.

Figures (1)

• Figure 1: Variation of the scalar spectral index $n_{s}$ as a function of $n \in (0,2)$ and $\sigma \in (0.00199622, 0.6263)$ for two fixed values of the parameter $\delta$. The left panel corresponds to $\delta =0.0002829$, where higher values of $\sigma$ are preferred for $n = 2$, resulting in $n_{s}$ values near the lower end of the observational range. The right panel corresponds to $\delta = 0.0111$, where lower values of $\sigma$ are favored, leading to $n_{s}$ values close to the upper observational limit. Both cases remain fully consistent with the current bounds from ACT data.