De Sitter-like configurations with asymptotic quintessence environment

TL;DR

This paper explores spherically symmetric spacetimes with vacuum energy influenced by an external quintessence field, leading to various solutions including de Sitter-like configurations that behave as slow-roll quintessence.

Contribution

It introduces a new class of solutions affected by a non-dynamical quintessence field, revealing their stability properties and their interpretation as slow-roll quintessence in asymptotic regimes.

Findings

Identifies isotropic de Sitter-like solutions as slow-roll quintessence.

Shows complex deformations are prone to instability.

Compares new solutions with de Sitter and Hayward models.

Abstract

We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to an \emph{isotropic de Sitter-like solution} that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state {parameter} near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.