Modified Gravity Framework for the Woods-Saxon Inflation: Theoretical Foundations and Observational Constraints

Abstract

We investigate an inflationary scenario within a modified gravity theory that extends the Einstein-Hilbert action through a non-minimal coupling between the inflaton $\varphi$ and the trace of the energy-momentum tensor $T$. This $f(\varphi )T$ 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 $a\lesssim 1$ and the modest coupling $\beta =0.1$, we obtain a scalar spectral index $n_s\approx 0.959$--$0.966$ 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 $f(\varphi )T$ 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.

22 pages, LaTeX, 1 figure

References in corpus (9)

• f(R,T) gravity
• The Standard Model Higgs boson as the inflaton
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• The Unity of Cosmological Attractors
• Planck, LHC, and $\alpha$-attractors
• The Inflationary Quartic Hilltop Model in a Modified Gravity and Its Comparison with the Observations
• Observational Restrictions and Slow-Roll D-brane Inflation in the Special $F(\varphi ,T)$ Gravity
• The Inflationary Dynamics with the Scalar-Tensor Model