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

Area of Science:

• Theoretical Physics
• Cosmology
• Statistical Mechanics

Background:

• Kaniadakis statistics provides a generalized framework for complex systems, particularly in relativistic scenarios.
• Kaniadakis (κ-deformed) entropy has been recently applied to gravitational and cosmological models, offering richer phenomenology than standard approaches.

Purpose of the Study:

• To review recent advances and explore future challenges of Kaniadakis statistics in gravity and cosmology.
• To investigate the implications of κ-entropy on Holographic Dark Energy, Entropic Gravity, Black Hole thermodynamics, and Loop Quantum Gravity.
• To study Big Bang Nucleosynthesis within Kaniadakis Cosmology and constrain the κ-parameter.

Main Methods:

• Review of existing literature on κ-entropy in various physics domains.
• Theoretical modeling of Big Bang Nucleosynthesis under Kaniadakis Cosmology.
• Constraining the κ-parameter by comparing model predictions with observational data (freeze-out temperature fluctuations, primordial abundances of Helium-4 and Deuterium).

Main Results:

• The review highlights the broad impact of κ-entropy across fundamental physics areas.
• Consistency checks between Kaniadakis Cosmology predictions and observational data allow for the constraint of the κ-parameter.
• The study evaluates the potential of the Kaniadakis framework to accurately describe the observed universe.

Conclusions:

• Kaniadakis statistics presents a promising avenue for developing advanced models in gravity and cosmology.
• The κ-parameter can be effectively constrained through cosmological observations like Big Bang Nucleosynthesis.
• Further research is warranted to fully explore the capabilities of Kaniadakis statistics in explaining cosmic phenomena.