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

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.