Research Information System
Annals of Physics, vol.485, 2026 (SCI-Expanded, Scopus)
Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard ΛCDM cosmological model. For example, exponential f(R) models often yield better fits to observational data, suggesting that ΛCDM may be inadequate. In this work, we argue that the gravitational and accelerating cosmology paradigm can remain close to GR and ΛCDM 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 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. We further show that these models can be endowed with relativistic versions of Perelman's thermodynamic variables for geometric flows, which we compute in general form for accelerating cosmology.