DBI analog of a decaying vacuum cosmology

TL;DR

This paper establishes a formal equivalence between k-essence scalar field cosmologies and decaying vacuum models, including a specific DBI model with exponential potential, broadening the understanding of their dynamical and thermodynamical relationships.

Contribution

It generalizes the equivalence between scalar field cosmologies and decaying vacuum models to non-canonical fields, introducing a formalism applicable to a wide class of models.

Findings

Derived a general formalism linking k-essence and decaying vacuum cosmologies.

Established the equivalence for a DBI model with exponential potential and constant sound speed.

Demonstrated the thermodynamical and dynamical consistency of the models.

Abstract

In this work I discuss the dynamical and thermodynamical equivalence between a general k-essence scalar field cosmology and an arbitrary cosmological model with a decaying vacuum, thus generalizing the approach proposed by Maia and Lima [Phys. Rev. D {\bf 65}, 083513 (2002)]. The formalism obtained is quite general and holds for any non-canonical scalar field model. As a special case I derive a Dirac-Born-Infeld (DBI) model with an exponential potential and constant speed of sound, and show that it is equivalent to a cosmological model with decay law $\Lambda(H) = 3\beta H^2$.