Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology

TL;DR

This paper explores off-diagonal solutions in Einstein gravity using AFCDM, showing they can replicate dark energy effects and MGT features within general relativity, thus challenging the need for alternative theories.

Contribution

It introduces the AFCDM method to construct off-diagonal Einstein solutions that mimic modified gravity and dark energy phenomena within GR.

Findings

Off-diagonal Einstein solutions can approximate MGT effects.

These solutions can model dark energy and dark matter phenomena.

The method enables decoupling of complex nonlinear PDEs in gravity.

Abstract

Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data, suggesting that Lambda CDM may be inadequate. In this work, we argue that the gravitational and accelerating cosmology paradigm can remain close to GR and Lambda CDM if one considers broader classes of off-diagonal cosmological solutions of the Einstein equations. These solutions are constructed using the anholonomic frame and connection deformation method (AFCDM), which enables the decoupling and integration of nonlinear systems of partial differential equations in nonholonomic dyadic variables with connection distortions. The resulting off-diagonal Einstein manifolds and cosmological models are characterized by nonholonomic constraints, nonlinear symmetries, and effective cosmological constants. Such structures allow one to approximate cosmological effects, mimic features of MGTs, and describe gravitational polarization, local anisotropies, and dark energy and dark matter phenomena within GR.