Modified gravity version of inflationary α-attractor models: dynamics, perturbations, and reheating

Abstract We investigate inflationary dynamics in a modified gravity framework with a nonminimal coupling $f(\phi)T$, where $T$ is the trace of the energy-momentum tensor. This coupling naturally emerges as a low-energy effective operator in $f(R,T)$ gravity and vanishes in the post-inflationary era ($\phi \to 0$), ensuring exact recovery of general relativity. Focusing on $\alpha$-attractor T-models with potential $V(\phi) = V_0 \tanh^2(\phi/\sqrt{6\alpha})$ and coupling $f(\phi) = f_0 \tanh(\phi/\sqrt{6\alpha})$, we derive the modified slow-roll parameters, cosmological perturbations, and stability conditions. The coupling shifts predictions toward larger scalar spectral index $n_s$ while maintaining a small tensor-to-scalar ratio $r$, accessing the right side of the Planck/BICEP/Keck observationally favored region. For $\beta=0.2$ and $\alpha=1.5$, we find $(n_s, r) = (0.9793, 0.0025)$ for $N=60$, within the $1\sigma$ Planck contour. A statistical analysis using Planck 2018 data yields $\beta = 0.28 \pm 0.09$ at $68\%$ CL. The modified coupling enhances the inflaton decay width, yielding a reheating temperature $T_{\rm reh} \sim 5.5 \times 10^{13}$ GeV, satisfying all BBN constraints. We also analyze preheating dynamics, stability conditions, gravitational wave propagation, and future experimental tests. This framework extends the reach of $\alpha$-attractors and offers a theoretically motivated bridge between modified gravity and inflationary cosmology.