  We develop a new approach to gravitational waves in which the Einstein
equations are governed by the cosmological constant which is related to the
existence of a manifold which is closed. We study an example in which the
matter Lagrangian is described by the scalar (inflaton) field. There are only
three dynamical solutions. In one of them the universe is initially static but
begins to increase until an inflationary stage. We calculate the dynamics of GW
in this primordial pre-inflationary stage of the universe. We found that there
should be an infinite number of polarization modes in order to the fields can
be quantized. Finally, we calculate the energy density due to the gravitational
waves.
