  It is proposed to consider dark matter as a perfect dilaton-spin fluid (with
particles endowed with intrinsic spin and dilaton charge) in the framework of a
gravitational theory with a Weyl-Cartan geometrical structure. The modified
Friedmann-Lema\^{\i}tre equation (with a cosmological term) is obtained for the
homogeneous and isotropic Universe filled with the dilaton-spin dark matter. On
the basis of this equation, we develop a nonsingular cosmological model
starting from an inflation-like stage (for super-stiff equation of state),
passing radiation-dominated and matter-dominated decelerating stages and
turning into a post-Friedmann accelerating era.
