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

We investigate inflationary dynamics in a modified gravity framework with a nonminimal coupling f(φ)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 (φ → 0), ensuring exact recovery of general relativity. Focusing on α-attractor T-models with potential V(φ) = V₀ ²(φ/√6α) and coupling f(φ) = f₀ (φ/√6α), we derive the modified slow-roll parameters, cosmological perturbations, and stability conditions. The coupling shifts predictions toward larger scalar spectral index nₛ while maintaining a small tensor-to-scalar ratio r, accessing the right side of the Planck/BICEP/Keck observationally favored region. For β=0.2 and α=1.5, we find (nₛ, r) = (0.9793, 0.0025) for $N=60$, within the 1σ Planck contour. A statistical analysis using Planck 2018 data yields β = 0.28 ± 0.09 at $68%$ CL. The modified coupling enhances the inflaton decay width, yielding a reheating temperature Tᵣₑₕ ~ 5.5 × 10¹³ 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 α-attractors and offers a theoretically motivated bridge between modified gravity and inflationary cosmology.