Dynamical Couplings, Dynamical Vacuum Energy and Confinement/Deconfinement from R^2-Gravity

TL;DR

This paper explores a modified gravity model with nonlinear gauge fields, revealing how confinement dynamics can vary across different regions and uncovering new black hole solutions with unique properties.

Contribution

It introduces a novel f(R)-gravity model with nonlinear gauge fields, demonstrating dynamical confinement and vacuum energy, and presents explicit solutions including new black hole types.

Findings

Confinement dynamics can disappear in flat regions of the effective potential.

Dynamical gauge couplings and cosmological constant emerge from the model.

New classes of black hole solutions with unique asymptotics are found.

Abstract

We study within Palatini formalism an f(R)-gravity with f(R)= R + \alpha R^2 interacting with a dilaton and a special kind of nonlinear gauge field system containing a square-root of the standard Maxwell term, which is known to produce confinement in flat space-time. Reformulating the model in the physical Einstein frame we find scalar field effective potential with a flat region where the confinement dynamics disappears, while in other regions it remains intact. The effective gauge couplings as well as the induced cosmological constant become dynamical. In particular, a conventional Maxwell kinetic term for the gauge field is dynamically generated even if absent in the original theory. We find few interesting classes of explicit solutions: (i) asymptotically (anti-)de Sitter black holes of non-standard type with additional confining vacuum electric potential even for the electrically neutral ones; (ii) non-standard Reissner-Nordstroem black holes with additional constant vacuum electric field and having non-flat-spacetime "hedgehog" asymptotics; (iii) generalized Levi-Civitta-Bertotti-Robinson "tube-like" space-times.