  This article is devoted to the study of the thermodynamics phase transitions
and critical phenomena of an FLRW cosmological model under the so-called
Kaniadakis's statistics. The equation of state is derived from the corrected
Friedmann field equations and the thermodynamics unified first law. This
reveals the existence of non-trivial critical points where a first-order phase
transition takes place. The system behaves as an "inverted" van der Waals fluid
in this concern. 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.
