Inconsistencies of Tsallis Cosmology within Horizon Thermodynamics and Holographic Scenarios
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| Format: | Preprint |
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2025
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| author | Ibarbo-Perlaza., Pedro M. Orjuela-Quintana, J. Bayron Palacios-Córdoba, Jose L. Valenzuela-Toledo, César A. |
| author_facet | Ibarbo-Perlaza., Pedro M. Orjuela-Quintana, J. Bayron Palacios-Córdoba, Jose L. Valenzuela-Toledo, César A. |
| contents | 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 $δ$, with the standard Bekenstein-Hawking entropy-area relation recovered for $δ= 1$. While previous studies have suggested that only small deviations from extensivity are observationally allowed, typically requiring $|1 - δ| \lesssim 10^{-3}$, here we go further and perform a systematic consistency analysis across the entire expansion history.
We show that even mild departures from $δ= 1$ 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 $Λ$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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inconsistencies of Tsallis Cosmology within Horizon Thermodynamics and Holographic Scenarios Ibarbo-Perlaza., Pedro M. Orjuela-Quintana, J. Bayron Palacios-Córdoba, Jose L. Valenzuela-Toledo, César A. Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology 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 $δ$, with the standard Bekenstein-Hawking entropy-area relation recovered for $δ= 1$. While previous studies have suggested that only small deviations from extensivity are observationally allowed, typically requiring $|1 - δ| \lesssim 10^{-3}$, here we go further and perform a systematic consistency analysis across the entire expansion history. We show that even mild departures from $δ= 1$ 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 $Λ$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. |
| title | Inconsistencies of Tsallis Cosmology within Horizon Thermodynamics and Holographic Scenarios |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.00234 |