Born-Infeld gravity and its functional extensions
We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that non-singular universes with a cosmic bounce are very generic and robust solutions.
Born-Infeld f(R) gravity
Motivated by the properties of matter quantum fields in curved space-times, we work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an $f(R)$ piece. To avoid ghost-like instabilities, the theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions such as the dynamics of the early universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an $f(R)=a R^2$ term has on the early-time cosmology. We find that bouncing solutions are robust against these modifications of the Lagrangian whereas the solutions with {\it loitering} behavior of the ori…
Little Rip, ΛCDM and singular dark energy cosmology from Born–Infeld-f(R) gravity
Abstract We study late-time cosmic accelerating dynamics from Born–Infeld- f ( R ) gravity in a simplified conformal approach. We find that a variety of cosmic effects such as Little Rip, ΛCDM universe and dark energy cosmology with finite-time future singularities may occur. Unlike the convenient Born–Infeld gravity where in the absence of matter only de Sitter expansion may emerge, apparently any FRW cosmology maybe reconstructed from this conformal version of the Born–Infeld- f ( R ) theory. Despite the fact that the explicit form of f ( R ) is fixed by the conformal ansatz, the relation between the two metrics in this approach may be changed so as to bring out any desired FRW cosmology.