Geometric methods for constructing cosmological solutions for EYMH systems in two measure, f(R) and massive gravity theories

A brief summary of the anholonomic frame deformation method, AFDM, for generating exact solutions with generic off-diagonal metrics and generalized nonlinear connections in modified gravity theories, MGTs, is presented. We generalize the method to systems of nonlinear partial differential equations, PDEs, for constructing solutions describing generalized (effective) Einstein-Yang-Mills-Higgs, EYMH, interactions in two measure, f(R) and massive gravity theories. Finally, we speculate on possible applications of such generalized anisotropic and inhomogeneous solutions in modern acceleration cosmology