Matter with dilaton charge in Weyl–Cartan spacetime and evolution of the universe

The perfect dilaton–spin fluid (as a model of the dilaton matter, the particles of which are endowed with intrinsic spin and dilaton charge) is considered as the source of the gravitational field in a Weyl–Cartan spacetime. The variational formalism of the gravitational field in a Weyl–Cartan spacetime is developed in the exterior form language. A homogeneous and isotropic universe filled with the dilaton matter as the dark matter is considered and one of the field equations is represented as the Einstein-like equation which leads to the modified Friedmann–Lemaître equation. From this equation the absence of the initial singularity in the cosmological solution follows. Also the existence of two points of inflection of the scale factor function is established, the first of which corresponds to the early stage of the universe and the second to the modern era when the expansion with deceleration is replaced by the expansion with acceleration. Possible equations of state for the self-interacting cold dark matter are found on the basis of the modern observational data. An inflation-like solution is obtained.