  We investigated the possibility of construction the homogeneous and isotropic
cosmological solutions in Weyl geometry. We derived the self-consistency
condition which ensures the conformal invariance of the complete set of
equations of motion. There is the special gauge in choosing the conformal
factor when the Weyl vector equals zero. In this gauge we found new vacuum
cosmological solutions absent in General Relativity. Also, we found new
solution in Weyl geometry for the radiation dominated universe with the
cosmological term, corresponding to the constant curvature scalar in our
special gauge. Possible relation of our results to the understanding both dark
matter and dark energy is discussed.
