Evading the Swampland de Sitter Obstruction via Thermodynamic Duality-Induced Horizon Corrections in Unimodular Gravity

Abstract

We investigate the early-universe cosmological implications of Unimodular Gravity coupled to Power-Law Nonlinear Electrodynamics in the presence of quantum-corrected horizon thermodynamics derived from the principle of thermodynamic duality. By incorporating both logarithmic and inverse-area corrections to the Bekenstein-Hawking entropy, we derive modified Friedmann equations exhibiting novel $H^4$ and $H^6$ terms that represent genuine quantum gravity effects. We demonstrate that these higher-order corrections become dynamically significant in the high-energy regime of cosmic inflation, naturally modifying the slow-roll dynamics without requiring a fundamental inflaton potential. A comprehensive phase-space analysis reveals that the quantum corrections drive early-time de Sitter-like attractors, providing a robust mechanism for sustained inflationary expansion. Confronting the model with the Swampland program, we show that the correction factor $\mathcal{F}(H)$ modifies the effective slow-roll parameters, enabling the model to satisfy the Swampland de Sitter and Distance conjectures during the inflationary epoch. We calculate the inflationary observables, including the spectral index $n_s$ and the tensor-to-scalar ratio $r$, and demonstrate that the model's predictions are in excellent agreement with the Planck 2018 observational constraints. Our results suggest that thermodynamic duality-induced horizon corrections offer a viable and testable pathway for realizing successful inflation within a well-motivated quantum-gravitational framework.