The classical cosmology of flat space can be realized in a phenomenological scalar field model for dark energy: a two-field model of quintessence and phantom fields. When the model is supplied by a proper field mixing term it becomes analytically solvable for exponential potentials. The motivation is given for replacing a phantom field by a normal pseudoscalar field with complex but PT-symmetric potential (PTom). The comparison of two approaches in their prediction for the fate of our Universe is done in figures. The quantum cosmology of flat space is realized in the Arnowitt-Deser-Misner approach by means of the Wheeler-DeWitt equations. Taking into account the isotropy and homogeneity of space the ADM approach is reduced to only quantized component of space-time metric—Friedmann-Robertson-Walker factor. The quantum models supplied with appropriate mixing kinetic terms turn out to be also integrable for exponential potentials and the exact analytical solutions are obtained for wave functionals of quantum PT