Metric gravity theories and cosmology. I. Physical interpretation and viability

Abstract

We critically review some concepts underlying current applications of gravity theories with Lagrangians depending on the full Riemann tensor to cosmology. We argue that it is impossible to reconstruct the underlying Lagrangian from the observational data: the Robertson-Walker spacetime is so simple and "flexible" that any cosmic evolution may be fitted by infinite number of Lagrangians. Confrontation of a solution with the astronomical data is obstructed by the existence of many frames of dynamical variables and the fact that initial data for the gravitational triplet depend on which frame is minimally coupled to ordinary matter. Prior to any application it is necessary to establish physical contents and viability of a given gravity theory.

29 pages. The previous version is divided in two separate papers. The first four chapters, expanded and modified, form the present paper. The title and abstract are adequately modified, some recent references added. The main conclusions remain unchanged. The second part will also appear in Class. Qu. Grav

References in corpus (17)

• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Are f(R) dark energy models cosmologically viable ?
• An improved limit on the axion-photon coupling from the CAST experiment
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Dynamics of Linear Perturbations in f(R) Gravity
• Limit to General Relativity in f(R) theories of gravity
• Solar System tests DO rule out 1/R gravity
• A f(R) gravity without cosmological constant
• f(R) actions, cosmic acceleration and local tests of gravity
• Solar system effects in Schwarzschild--de Sitter spacetime
• Viability of f(R) Theories with Additional Powers of Curvature
• Solar System planetary orbital motions and f(R) Theories of Gravity
• The accelerating universe and a limiting curvature proposal
• Late-time oscillatory behaviour for self-gravitating scalar fields
• Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
• On the issue of gravitons

Cited by in corpus (40)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• f(R,T) gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• f(R,L_m) gravity
• Wormhole geometries in f(R) modified theories of gravity
• Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases
• Modified gravity with arbitrary coupling between matter and geometry
• On the LCDM Universe in f(R) gravity
• $f(R,T_{\mu \nu }{T}^{\mu \nu })$ gravity and Cardassian-like expansion as one of its consequences
• Energy conditions in $f(R,G)$ gravity
• Collapsing spherical stars in f(R) gravity
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Thin accretion disks in f(R) modified gravity models
• Stability of the Einstein static universe in f(R) gravity
• Energy conditions in modified Gauss-Bonnet gravity
• Black hole solutions in F(R) gravity with conformal anomaly
• On the Stability of a class of Modified Gravitational Models
• Exact solutions of f(R) gravity coupled to nonlinear electrodynamics
• Power-law cosmic expansion in f(R) gravity models
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Weyl-Cartan-Weitzenböck gravity as a generalization of teleparallel gravity
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• Accelerating Universe in Modified Theories of Gravity
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• f(R) gravity: successes and challenges
• Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars
• Cosmological dynamics of fourth order gravity: A compact view
• Perihelion precession for modified Newtonian gravity
• "Detuned" f(R) gravity and dark energy
• Homogeneous cosmologies in generalized modified gravity
• Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy
• Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories
• Cosmic acceleration and $f(R)$ theory: perturbed solution in a matter FLRW model
• Oscillatory behavior of closed isotropic models in second order gravity theory
• Multipole analysis for linearized $f(R,\mathcal{G})$ gravity with irreducible Cartesian tensors
• Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors
• Test-field limit of metric nonlinear gravity theories