Geometric roots of the cosmology model

Abstract

Arising of interest in solving of soliton equations in (1+1)-dimension made some progress in developing of mathematics, particularly, differential geometry. Lack of geometric charachteristics are appeared in undestanding of soliton solution. In this context, we give geometric explanation of the investigated model. We consider gravity theory with a metric-dependent on torsion, so-called F(R; T) gravity [1]-[2]. We research geometric roots of the theory. In particular, we represent the model with geometric point of view. Moreover, the general form of F(R; T) gravity with two arbitrarly functions is represented. It is considered in the case of Fridmann-Robertson-Walker spatially flat metric. Contortion components are found by defining of non-vanishing torsion components and Levi-Civita connections. Similarly nonvanishing Ricci curvature components are found. Finally, the explicit forms of curvature and torsion scalars are represented.