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 (56)

• f(R) Theories Of Gravity
• f(R) theories
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Disappearing cosmological constant in f(R) gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Can modified gravity explain accelerated cosmic expansion?
• 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
• The Relation between Physical and Gravitational Geometry
• On Physical Equivalence between Nonlinear Gravity Theories
• Nonlocal Cosmology
• Einstein-Aether Waves
• Eddington's theory of gravity and its progeny
• Covariant conservation of energy momentum in modified gravities
• Metric-affine f(R) theories of gravity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Accelerated Cosmological Models in Ricci squared Gravity
• Matter instability in modified gravity
• Cosmological perturbations in the Palatini formulation of modified gravity
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• The matter power spectrum in f(R) gravity
• Effective Lagrangians and Universality Classes of Nonlinear Bigravity
• 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
• Dark energy from modified gravity with Lagrange multipliers
• 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
• Vector field models of modified gravity and the dark sector
• Conformal aspects of Palatini approach in Extended Theories of Gravity
• Disformal Scalar Fields and the Dark Sector of the Universe
• Nonlocal gravity and the diffusion equation
• Viable Singularity-Free f(R) Gravity Without a Cosmological Constant
• Curvature scalar instability in f(R) gravity
• Viable Palatini-f(R) cosmologies with generalized dark matter
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• The Cauchy problem of f(R) gravity
• How (Not) to Palatini
• Cosmology of modified (but second order) gravity
• Cosmic acceleration and crossing of w=-1 barrier in non-local Cubic Superstring Field Theory model
• A New Formulation of the Initial Value Problem for Nonlocal Theories
• Comments on scalar-tensor representation of nonlocally corrected gravity
• The dynamics of generalized Palatini Theories of Gravity
• From Dark Energy and Dark Matter to Dark Metric
• A note on bigravity and dark matter
• The dynamical Casimir effect in braneworlds
• Bouncing Palatini cosmologies and their perturbations
• Variational and conformal structure of nonlinear metric-connection gravitational lagrangians

Cited by in corpus (54)

• Modified Gravity and Cosmology
• Extended Theories of Gravity
• f(R,T) gravity
• Cosmology in $f(Q)$ geometry
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• Wormhole geometries in modified teleparralel gravity and the energy conditions
• Teleparallel Palatini theories
• Wormholes supported by hybrid metric-Palatini gravity
• Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration
• Higgs-Palatini Inflation and Unitarity
• Hybrid metric-Palatini gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Generalized hybrid metric-Palatini gravity
• Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications
• Extended Gauss-Bonnet gravities in Weyl geometry
• Bimetric gravity doubly coupled to matter: theory and cosmological implications
• Hybrid modified gravity unifying local tests, galactic dynamics and late-time cosmic acceleration
• Inflation and non-minimal scalar-curvature coupling in gravity and supergravity
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• Scale transformations in metric-affine geometry
• On new variational principles as alternatives to the Palatini method
• Palatini-Higgs inflation with non-minimal derivative coupling
• Hybrid metric-Palatini stars
• Ghosts in pure and hybrid formalisms of gravity theories: a unified analysis
• Linear growth of structure in massive bigravity
• The bimetric variational principle for General Relativity
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Cosmology for quadratic gravity in generalized Weyl geometry
• Dark D-brane Cosmology
• Palatini frames in scalar-tensor theories of gravity
• On the consistency of non-minimally coupled f(R) gravity
• The post-Newtonian limit in C-theories of gravitation
• Multi-Scalar-Tensor Equivalents for Modified Gravitational Actions
• Cosmological phase space of generalized hybrid metric-Palatini theories of gravity
• Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity
• Non-locality of the C- and D-theories
• ADM Analysis of Gravity Models within the Framework of Bimetric Variational Formalism
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• An axiomatic purification of gravity
• Non-metric chaotic inflation
• Transit String Dark Energy Models in $f(Q)$ Gravity
• Variational approach to gravitational theories with two independent connections
• Thermodynamics of Evolving Lorentzian Wormholes at Apparent Horizon in $f(R)$ Theory of Gravity
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• Hybrid metric-Palatini brane system
• Matters on a moving brane
• A modified variational principle for gravity in modified Weyl geometry
• Binary systems in Palatini-f(R) gravity
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• The cosmological constant filter without big bang singularity
• Comparing metric and Palatini approaches to vector Horndeski theory
• Novel aspects of C-theories in Cosmology
• Effectively nonlocal metric-affine gravity
• Quintessence dark energy model in non-linear $f(Q)$ theory with bulk-viscosity