Effective Einstein Cosmological Spaces for Non-Minimal Modified Gravity

Abstract

Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ type. We prove this statement by constructing exact and approximate solutions which encode certain models of covariant Ho\v rava type gravity with dynamical Lorentz symmetry breaking. Off-diagonal generalizations of de Sitter and nonolonomic $\Lambda$CDM universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is discussed.

Title changed and length drastically reduced at the requests of GRG editors

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• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• Physical Parameters for Stable $f(R)$ Models
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• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
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• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• 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
• Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models
• 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
• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures