Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges

Abstract

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis (κ-deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell–Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of κ-entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of 4He and D, we constrain the free κ-parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe.

Constraining Barrow entropy-based Cosmology with power-law inflation

“…Preliminary investigation in this direction has been proposed in [55] in the context of both Tsallis and Barrow entropies, showing that the entropic deformation parameter significantly influences the growth of perturbations. Moreover, one can attempt to extend the present considerations to Cosmology based on Kaniadakis entropy [56], which is a self-consistent relativistic generalization of Boltzmann-Gibbs entropy with non-trivial cosmological implications [57]. In this way, a relationship between Barrow and Kaniadakis formalisms can be established.…”

Saez-Ballester gravity in Kantowski-Sachs Universe: a new reconstruction paradigm for Barrow Holographic Dark Energy

“…-A further challenging perspective is to extend the present analysis to the case of HDE based on Kaniadakis entropy [35] (Kaniadakis Holographic Dark Energy, KHDE) which is a self-consistent relativistic generalization of Boltzmann-Gibbs entropy parameterized by −1 < K < 1 [98,99]. In this context, it would be interesting to find any connection between BHDE and KHDE or, at a more fundamental level, any relation between Barrow and Kaniadakis deformation parameters.…”

From the emergence of cosmic space to horizon thermodynamics in Barrow entropy-based Cosmology

“…Moreover, since our model attempts to embed quantum gravitational corrections into Cosmology via Barrow entropy, it is important to study the present results comparing to predictions from more fundamental candidate theories of quantum gravity, such as String Theory of Loop Quantum Gravity. Finally, we aim at extending our analysis to the case of other deformed entropies, in particular to Kaniadakis entropy [62,63], which arises from a coherent and self-consistent relativistic generalization of the classical Boltzmann-Gibbs-Shannon entropy. Work along these and other directions is currently under investigation and will be presented elsewhere.…”