Cosmology of non-Hermitian (C)PT-invariant scalar matter

We use the generalization of quantum theory for the case of non-Hermitian Hamiltonians with (C)PT symmetry to show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. We consider the PT symmetric flat Friedmann model of two scalar fields with positive kinetic terms. The solution for the normal field is real while the solution for the second field is purely imaginary, realizing classically the 'phantom' behavior. The energy density and pressure happen to be real and the corresponding geometry is well-defined. The Lagrangian for the linear perturbations leads to positive energy densities for both the fields, so that the problem of stability does not arise. The phantom phase in the cosmological evolution appears to be transient and the Big Rip never occurs.