On the dynamics of cosmological phase transition during Bose–Einstein condensation of dark matter in Barrow entropy-based cosmology

Abstract Throughout the cosmic evolution of the Universe, when the temperature of a boson gas drops below a certain threshold, the Bose–Einstein condensation phenomenon may occur. In this scenario, the dark matter, viewed as a non-relativistic Newtonian gravitational condensate, is described by the Gross–Pitaevskii–Poisson system. Our research explores the evolution dynamics of the Bose–Einstein condensation of bosonic dark matter, considering it as an approximate first-order phase transition within a quantum gravitational-corrected cosmological setting referred to as Barrow entropy-based cosmology, which reflects the fractal nature of horizon geometry. We assess the quantities that characterize the dynamics of the Universe, such as temperature, energy density, scale factor, redshift, Hubble parameter, and deceleration parameter, before, during, and after the Bose–Einstein condensation phase crossover. Moreover, we specifically focus on the period of co-existence of normal and condensate phases of dark matter. We analyze the temporal behavior of an important parameter known as the condensate dark matter fraction throughout the condensation process and determine the duration of dark matter condensation. Our findings indicate that incorporating Bose–Einstein condensate dark matter within the framework of Barrow-modified cosmology significantly impacts the cosmic evolution of the Universe compared to the standard cosmological model. For a typical value of the Barrow exponent $$\delta = -1.3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1.3</mml:mn> </mml:mrow> </mml:math> , our model can account for an accelerated Universe without including a dark energy component and also addresses the age problem of our Universe. The negative value of $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> speculates a spongy or porous structure for the cosmological horizon geometry at the Planck scale.