Inconsistencies of Tsallis Cosmology within Horizon Thermodynamics and Holographic Scenarios
arXiv:2510.00234 · doi:10.1103/n46p-zd3j
Abstract
We investigate the cosmological implications of Tsallis entropy in two widely discussed frameworks: the Cai-Kim thermodynamic derivation of the Friedman equations and the Tsallis holographic dark energy (HDE) scenario, considering both the Hubble scale and the Granda-Oliveros (GO) cutoff as infrared regulators. In both cases, the dynamics introduce a nonextensivity parameter , with the standard Bekenstein-Hawking entropy-area relation recovered for . While previous studies have suggested that only small deviations from extensivity are observationally allowed, typically requiring , here we go further and perform a systematic consistency analysis across the entire expansion history. We show that even mild departures from lead to pathological behavior in the effective dark energy sector: its density can become negative or complex, its equation of state may diverge, or it can contribute an unacceptably large early-time fraction that spoils radiation domination and violates BBN and CMB constraints. Our results sharpen and unify earlier hints of tension, providing a clear physical interpretation in terms of corrections that grow uncontrollably with the expansion rate toward the past. We conclude that within both the Cai-Kim and HDE formulations, a viable cosmology emerges only in the extensive limit, effectively reducing the models to CDM. More broadly, our findings emphasize the importance of dynamical consistency and cosmological viability tests, when assessing nonextensive entropy formalisms as potential frameworks for describing the Universe's dynamics.
Accepted for publication in Physical Review D