Gonzalo J. Olmo

Palatini Approach to Modified Gravity: f(R) Theories and Beyond

We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein’s theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

The Gravity Lagrangian according to solar system experiments

In this work we show that the gravity Lagrangian at relatively low curvatures in both metric and Palatini formalisms is a bounded function that can only depart from the linearity within the limits defined by well-known functions. We obtain those functions by analyzing a set of inequalities that any theory must satisfy in order to be compatible with laboratory and solar system observational constraints. This result implies that the recently suggested f(R)gravity theories with nonlinear terms that dominate at low curvatures are incompatible with observations and, therefore, cannot represent a valid mechanism to justify the cosmic speedup.

Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism

We compute the complete post-Newtonian limit of the metric form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.

Limit to general relativity in f(R) theories of gravity

We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity, f(R){yields}R. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original f(R) representation, solve the linearized equations, and compare our results with recent calculations of the literature. We observe that the linearized solutions are strongly affected by the cosmic evolution, which makes very unlikely that the cosmic speedup be due to f(R) models with correcting terms relevant at low curvatures.

Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration

We present a novel approach to modified theories of gravity which consists of adding to the Einstein- Hilbert Lagrangian an fðRÞ term constructed ala Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show that the theory can pass the Solar System observational constraints even if the scalar field is very light. This implies the existence of a long-range scalar field, which is able to modify the cosmological and galactic dynamics but leaves the Solar System unaffected. We also verify the absence of instabilities in perturbations and provide explicit models which are consistent with local tests and lead to the late-time cosmic acceleration.

Palatini f ( R ) black holes in nonlinear electrodynamics

The electrically charged Born-Infeld black holes in the Palatini formalism for

Bouncing cosmologies in Palatini f(R) gravity

f(R)

Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

theories are analyzed. Specifically we study those supported by a theory

Geonic black holes and remnants in Eddington-inspired Born–Infeld gravity

f(R)=R\ifmmode\pm\else\textpm\fi{}{R}^{2}/{R}_{P}

Dynamical Aspects of Generalized Palatini Theories of Gravity

, where