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

TL;DR

This paper constructs and analyzes off-diagonal cosmological solutions in massive gravity, showing how they can model dark energy, dark matter, and cyclic or ekpyrotic universes with observable signatures.

Contribution

It introduces a new method for generating off-diagonal solutions in massive gravity and demonstrates their potential to explain cosmological phenomena like dark energy and cyclic universes.

Findings

New classes of anisotropic cosmological metrics are constructed.

Solutions can mimic general relativity and modified gravity solutions.

Reconstruction of cyclic and ekpyrotic universe models is achieved.

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-Lama\^itre-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 Painlev\'e--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.