  New one parameter family of exact solutions in General Relativity with a
scalar field is found. The metric is of Liouville type which admits complete
separation of variables in the geodesic Hamilton--Jacobi equation. This
solution exists for the exponential potential for a scalar field and is
invariant with respect to global Lorentz transformations. It describes, in
particular, a black hole formation as well as a naked singularity. Solutions
corresponding to the naked singularity describe accelerating expansion of the
homogeneous and isotropic Universe, and can be smoothly continued along
geodesics to infinite past without Big Bang.
