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

Understand

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.