On a free Dirac–Born–Infeld interacting vacuum model

Abstract In this paper, we will propose a novel interacting vacuum model whose energy flow is modeled according to the free Dirac–Born–Infeld theory and hydrodynamically realized via the (Modified) Berthelot equation of state. By employing dynamical system techniques, we will identify a suitable late-time attractor which can realistically account for the present-day configuration of the universe, addressing the coincidence problem, supporting an accelerated expansion without breaking any energy condition, free from fine-tuning issues on initial conditions, and stable also at the perturbative level. Analytical closed-form results for the redshift evolution of both vacuum energy and dark matter will be presented. We will provide as well two distinctive fingerprints of our model, useful for its sharp identification inside the rich zoo of literature interacting vacuum models: a vacuum equation of state via geometric curvature scalars, and an analytical relationship between the statefinder variables. We will eventually show that our scenario actually consists in a running (or decaying) vacuum, with consequent production of dark matter particles, also comparing and contrasting its cosmological applicability with that of other known interacting vacuum paradigms. Our work therefore belongs to the line of research scrutinizing the relevance of quantum field theory approaches to the taming of current observational tensions.