A new approach to $P-V$ phase transitions: Einstein gravity and holographic type dark energy

In the framework of Einstein’s gravity, we study the thermodynamic equation state, $P=P(V,T)$, associated with a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. In this scenario, we consider the components of the dark sector as non-interacting fluids that dominate the universe’s energy content at late times. Under these circumstances, the functional structure of the cosmological coincidence parameter plays a relevant role in admitting first-order $P-V$ phase transitions; specifically, the dark energy density and the coincidence parameter must be given in terms of the radius of the apparent horizon.