Equivalent off-diagonal cosmological models and ekpyrotic scenarios in f(R)-modified, massive and Einstein gravity

Abstract

We re-investigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. There are constructed new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. By resorting such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related St\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lama\^ıtre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not obligatory always to modify gravity if we consider effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlev\' e-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, there are discussed open issues and further perspectives.

16 pages, latex2e; it is a regular article variant extended and modified following requests of the Editor and accepted by EPJC; this version contains new results and details comparing to the letter variant arXiv:1304.1080

References in corpus (9)

• Resummation of Massive Gravity
• New Ekpyrotic Cosmology
• Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution
• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Reconstruction of Scalar Potentials in Modified Gravity Models
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Scale Symmetry Breaking From Total Derivative Densities and the Cosmological Constant Problem
• Einstein Spaces Modeling Nonminimal Modified Gravity

Cited by in corpus (5)

• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Einstein Spaces Modeling Nonminimal Modified Gravity