Constant roll inflationary dynamics with generalized potentials in f(R,ϕ,X) gravity

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 ns 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 ns, 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.