  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 theory of such fluid is constructed and the dilaton-spin fluid
energy-momentum tensor is obtained. The variational formalism of the
gravitational field in a Weyl-Cartan spacetime ia developed in the exterior
form language. The homogeneous and isotropic Universe filled with the dilaton
matter as the dark matter is considered and one of the field equations is
represented as Einstein-like equation which leads to the modified
Friedmann-Lemaitre 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 one
corresponds to the modern era when the expansion with deceleration is replaced
by the expansion with acceleration. The possible equations of state for the
self-interacting cold dark matter are found on the basis of the modern
observational data. The inflation-like solution is obtained.
