Abstract 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 O (10^2), 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.
Taghavi et al. (Thu,) studied this question.