Phase transition in Schwarzschild-de Sitter spacetime

TL;DR

This paper investigates phase transitions in Schwarzschild-de Sitter spacetime by analyzing scalar fields near horizons, revealing conditions under which matter behaves as dark energy, suggesting a transition from dark matter to dark energy.

Contribution

It introduces a new constraint on the scalar field coupling constant and proposes a unified scenario for dark matter and dark energy based on horizon behavior.

Findings

Scalar field behaves as dust near horizons.

Coupling-dependent pressure to energy density ratio is derived.

Negative pressure near horizons implies coupling constant less than 1/4.

Abstract

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state(E.O.S) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de-Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally couplling this ratio is -1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be $\xi<{1/4}$ >. Therefore we derive a new constraint on the value of our coupling $\xi$ . These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.