MG12 - Talk detail
 

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Abstract

Enriched phenomenology in extended Palatini theories.

We study the field equations of $f(R,R_{\mu\nu}R^{\mu\nu})$ Palatini theories of gravity and provide an algorithm to solve for the independent connection for arbitrary lagrangian. We find that, in particular cases of interest, the physical metric and the metric associated with the independent connection are related by means of a disformal transformation. This relation between physical and auxiliary metric becomes conformal in the case of f(R) theories. We also show with explicit models that the inclusion of Ricci squared terms in the action can impose upper bounds on the accessible values of pressure and density, which might have important consequences for the early time cosmology and black hole formation scenarios. Our results indicate that the phenomenology of these theories is much richer than that of f(R) and f(R_{\mu\nu}R^{\mu\nu}) theories and that they also share some similarities with Bekenstein's relativistic theory of MOND.

Avoiding the Big Bang singularity with Palatini f(R) theories.

We discuss the conditions that guarantee the existence of homogeneous and isotropic models that avoid the Big Bang singularity in $f(R)$ theories in Palatini formalism. We show that for such models the Big Bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for presureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law lagrangians with a finite number of terms may lead to non-singular universes, which contrasts with the infinite-series Palatini $f(R)$ lagrangian that one needs to fully capture the effective dynamics of Loop Quantum Cosmology.

Static spherically symmetric solutions in extended Palatini gravity.

We consider static spherically symmetric configurations in a family of Palatini theories of gravity in which the lagrangian is an unspecified function of the form $f(R,R_{\mu\nu}R^{\mu\nu})$. We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of $f(R)$ theories and General Relativity in the appropriate limits. We show that exact interior solutions can be found for simple matter distributions and that the exterior solution is always of Schwarzschild-de Sitter type.

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