Unifying Einstein and Palatini gravities

Abstract

We consider a novel class of $f(\mathbb{R})$ gravity theories where the connection is related to the conformally scaled metric ${\hat{g}}_{\mu \nu }=C(\mathbb{R})g_{\mu \nu }$ with a scaling that depends on the scalar curvature $\mathbb{R}$ 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 $f(\mathbb{R})=\mathbb{R}$. With nonlinear $f(\mathbb{R})$, 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.

17 pages, no figures

References in corpus (27)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Metric-affine f(R) theories of gravity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Matter instability in modified gravity
• The matter power spectrum in f(R) gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Dynamics of Nonlocal Cosmology
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• On the evolution of density perturbations in f(R) theories of gravity
• Reconstructing the Distortion Function for Nonlocal Cosmology
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Newtonian limit of nonlocal cosmology
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Curvature scalar instability in f(R) gravity
• Viable Palatini-f(R) cosmologies with generalized dark matter
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• How (Not) to Palatini
• The Cauchy problem of f(R) gravity
• From Dark Energy and Dark Matter to Dark Metric
• A note on bigravity and dark matter
• The dynamical Casimir effect in braneworlds

Cited by in corpus (3)

• f(R,T) gravity
• Higgs-Palatini Inflation and Unitarity
• On new variational principles as alternatives to the Palatini method