Off-Diagonal Ekpyrotic Scenarios and Equivalence of Modified, Massive and/or Einstein Gravity

Abstract

Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related St\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé--ullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.

latex2e, 12pt, 12 pages, v4 with up-dated affiliations and substantial modifications requested by editor and referee and accepted by Phys. Lett. B

References in corpus (11)

• Resummation of Massive Gravity
• Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution
• New Cosmological Solutions in Massive Gravity
• Ghost-free $F(R)$ bigravity and accelerating cosmology
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
• Ghost-Free Massive $f(R)$ Theories Modelled as Effective Einstein Spaces and Cosmic Acceleration
• Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects
• Covariant Renormalizable Modified and Massive Gravity Theories on (Non) Commutative Tangent Lorentz Bundles

Cited by in corpus (20)

• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
• Equivalent off-diagonal cosmological models and ekpyrotic scenarios in f(R)-modified, massive and Einstein gravity
• 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
• Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry
• Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
• 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
• Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models
• Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology
• Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions