First-order phase transitions and cosmic evolution: thermodynamic approach to generalized holographic dark energy

Abstract Focusing on the description of cosmic evolution at late times, this study examines a generalized holographic dark energy (HDE) framework constructed via a polynomial expansion in the Hubble parameter, which includes contributions proportional to $$H^{2},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> $$H^{4},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> and $$H^{6},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>6</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> introduced through a variable parameter within the standard holographic formula. The analysis is carried out in the context of a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe, consisting of non-interacting matter together with the HDE fluid. We obtain the full set of Friedmann equations to investigate cosmic evolution and then analyze the system to determine whether thermodynamic $$P{-}v$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo>-</mml:mo> <mml:mi>v</mml:mi> </mml:mrow> </mml:math> type phase transitions can occur.