Tsallis holographic inflation in f ( R , T ) gravity: Planck/ACT constraints, reheating dynamics, and swampland bounds

In this work, we develop an inflationary scenario in which Tsallis holographic dark energy (THDE) provides an effective inflaton potential driving early-universe inflation within f(R, T) gravity. Adopting the Granda-Oliveros infrared cutoff, we derive the slow-roll relations and delineate a viable region of the parameter space (α, β, δ, λ) consistent with the Planck-ACT low-band combined likelihood (P-ACT-LB) from ACT DR6. Exploiting the parametric dependence of the THDE density on the Hubble expansion rate, we reconstruct the effective inflaton potential V(φ) across the observable window. We show that both the inflaton field excursion and the potential gradient |V′|/(VMp) are predominantly controlled by the matter-geometry coupling λ. In particular, for λ O(10²), the field excursion is suppressed below the Planck scale while ensuring |V|/(V Mₚ) O(1), consistent with the distance conjecture and the refined de Sitter swampland bound. We further investigate the reheating phase following inflation. In addition to the primordial nucleosynthesis requirement TBBN ≃ 4 MeV, the observational bound ΔNeff ≤ 0.17 imposes an additional lower limit on the reheating temperature through the integrated contribution of primordial gravitational waves (PGWs). During stiff reheating stages with ωre > 1/3, the high-frequency PGW spectrum is significantly enhanced, potentially leading to observable signatures in the frequency bands of forthcoming gravitational-wave detectors. For suitable parameter values, the resulting PGW signal may enter the projected sensitivity range of upcoming experiments. Overall, this work presents a unified and observationally consistent realization of holographic inflation in f(R, T) gravity, jointly constrained by CMB observations, reheating dynamics, primordial gravitational waves, and swampland bounds.