Modified gravity framework for the Woods-Saxon inflation: Theoretical foundations and observational constraints

We investigate an inflationary scenario within a modified gravity theory that extends the Einstein–Hilbert action through a non-minimal coupling between the inflaton ϕ and the trace of the energy–momentum tensor T . This f ( ϕ ) T framework is designed to naturally recover the standard general relativity in the post-inflationary universe. Within this theory, we apply the Woods-Saxon potential. The slow-roll dynamics yields a luminal sound speed c s 2 = 1 for our specific choice of the coupling function. For the model parameters a ≲ 1 and the modest coupling β = 0.1 , we obtain a scalar spectral index n s ≈ 0.959 –0.966 and a tensor-to-scalar ratio r < 0.01 , which reveal a good agreement with the latest Planck and BICEP/Keck data on the ( n s , r ) constraints. Crucially, we shall demonstrate that the f ( ϕ ) T coupling is essential for the observational viability of the model with respect to the CMB two-point statistics. This work establishes a viable inflationary scenario within the scope of the inflationary observables which are considered here.