Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics

This article studies the thermodynamics phase transitions and critical phenomena of an FLRW cosmological model under truncated Kaniadakis's statistics. The EoS is derived from the corrected Friedmann field equations and the thermodynamics unified first law. To approach thermodynamics, we use an approximation for KSAH≪1, on the cosmological equation, and also check the validity of our approximation. Then for different values from Kaniadakis parameter K, order O(10−37) for the relic-abundance, O(10−84) for 7Li-abundance and O(10−125) in the recombination era, the EoS reveals non-trivial critical points where a first-order phase transition occurs a sort of a van der Waals fluid. Interestingly, the numerical values of the critical exponents are the same as those of the van der Waals system. Besides, to obtain more insights into the thermodynamics description, the so-called Ruppeiner's geometry is studied through the normalized scalar curvature, disclosing this invariant zone where the system undergoes repulsive/attractive interactions. Near the critical point, this curvature provides again the same critical exponent and universal constant value as for van der Waals fluid. Despite the similarity, both systems are quite different because the present one considers a relativistic entropy (Kaniadakis entropy) while the Van der Waals gas responds to a classical entropy (Maxwell-Boltzmann).