Unifying Einstein and Palatini gravities

Details Unifying Einstein and Palatini gravities Unifying Einstein and Palatini gravities

2010-10-22

arxiv.org/abs/1010.4776v1

Phys.Rev.D83:044016,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, no figures

Scientific paper

10.1103/PhysRevD.83.044016

We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, C-theories include completely new physically distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$, C-theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show that C-theories have a scalar-tensor formulation, which in some special cases reduces to simple Brans-Dicke-type gravity. If matter fields couple to the connection, the conservation laws in C-theories are modified. The stability of perturbations about flat space is determined by a simple condition on the lagrangian.

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