Was there a Big Bang?

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, evolution of the space-time with the naked singularity. Solutions corresponding to the naked singularity provide accelerating expansion of the homogeneous and isotropic Universe, and can be smoothly continued along geodesics to infinite past without Big Bang.