Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
arXiv:2106.00462 · doi:10.3390/universe7040089
Abstract
We study new classes of generic off-diagonal and diagonal cosmological solutions for effective Einstein equations in modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding possible violations of (local) Lorentz invariance, LIVs. Such MGTs are constructed for Lagrange densities with two non-Riemannian volume forms (two-measure theories, TMTs) and associated bimetric/ biconnection geometric structures. For conventional 2+2 splitting, we can describe such models in Finsler like variables, which is important for elaborating geometric methods of constructing exact and parametric solutions. Such formulations of general relativity, GR, and MGTs are considered for Lorentz manifolds and their (co) tangent bundles, in brief, FTMT. Off-diagonal metrics solving gravitational field equations in FTMTs are determined by generating functions, effective sources and integration constants and characterized by nonholonomic frame torsion effects. Restricting the class of integration functions, we can extract torsionless and diagonal configurations and model emergent cosmological theories with square scalar curvature, , when the global Weyl-scale symmetry is broken via nonlinear dynamical interactions with nonholonomic constraints. In the physical Einstein-Finsler frame, the constructions involve (i) nonlinear re-parametrization symmetries of the generating functions and effective sources; (ii) effective potentials for the scalar field with possible two flat regions which allows a unified description of locally anisotropic and/or isotropic early universe inflation related to acceleration cosmology and dark energy; (iii) there are "emergent universes" described by (off-) diagonal solutions for certain nonholonomic phases and parametric cosmological evolution resulting in various inflationary phases; (iv) we can reproduce in two-measure theories massive gravity effects.
latex2e, 30 pages, v2 contains a new subsection 7.2 introduced on request of journal's editor and extends v1, arXiv: submit/36467, from March 12, 2021
References in corpus (13)
- Resummation of Massive Gravity
- Emergent Universe with Exotic Matter
- Emergent Cosmology, Inflation and Dark Energy
- A graceful entrance to braneworld inflation
- A two measure model of dark energy and dark matter
- Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
- Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
- Dynamics in Varying vacuum Finsler-Randers Cosmology
- Bounce cosmology in generalized modified gravities
- Relativistic kinetic gases as direct sources of gravity
- Scale Symmetry Breaking From Total Derivative Densities and the Cosmological Constant Problem
- On the analyticity of static solutions of a field equation in Finsler gravity
- Dark Gravitational Field on Riemannian and Sasaki Spacetime