Abstract
We apply the gravity-thermodynamics conjecture, namely the first law of thermodynamics on the Universe horizon, but using the generalized Kaniadakis entropy instead of the standard Bekenstein–Hawking one. The former is a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy, arising from a coherent and self-consistent relativistic statistical theory. We obtain new modified cosmological scenarios, namely modified Friedmann equations, which contain new extra terms that constitute an effective dark energy sector depending on the single model Kaniadakis parameter K. We investigate the cosmological evolution, by extracting analytical expressions for the dark energy density and equation-of-state parameters and we show that the Universe exhibits the usual thermal history, with a transition redshift from deceleration to acceleration at around 0.6. Furthermore, depending on the value of K, the dark energy equation-of-state parameter deviates from Lambda CDM cosmology at small redshifts, while lying always in the phantom regime, and at asymptotically large times the Universe always results in a dark-energy dominated, de Sitter phase. Finally, even in the case where we do not consider an explicit cosmological constant the resulting cosmology is very interesting and in agreement with the observed behavior.
Highlights
Beyond the aforementioned directions in constructing new modified theories, there is a well-known conjecture that gravity can be expressed within laws of thermodynamics [30–32]
The plan of the manuscript is the following: In Sect. 2 we briefly review the application of the aforementioned conjecture in cosmology, and we present the new constructed modified scenario arising from the generalized Kaniadakis entropy instead of the usual Bekenstein–Hawking one
In this work we have constructed new cosmological scenarios by considering the widely-known conjecture that thermodynamics is related to gravity
Summary
Beyond the aforementioned directions in constructing new modified theories, there is a well-known conjecture that gravity can be expressed within laws of thermodynamics [30–32]. C (2021) 81:1037 tions have been considered in the literature, such as Sharma– Mittal entropy [52], Rényi entropy [53], Shannon entropy [54], non-additive Tsallis entropy [55,56], Barrow entropy [57], etc, all of which possess the standard entropy as a particular limit One interesting such case of generalized entropy is Kaniadakis entropy [58,59]. This is a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy, arising from a coherent and self-consistent relativistic statistical theory, which preserves the basic features of standard statistical theory, and recovers it in a particular limit. We will apply the first law of thermodynamics in the Universe horizon, but using Kaniadakis entropy for the horizon entropy In this way we obtain modified Friedmann equations, in which the new extra terms will constitute the pillar for our investigation of the cosmological implications.
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