On Virtual Scalar Fields in a Conformally Flat FLRW Spacetime

The case of a virtual bosonic scalar field phi(x) gravitationally coupled in a conformally flat spacetime is investigated. The action S is known to be Weyl invariant only for specific expressions of the potential V(phi). In the conformally flat FLRW case the harmonic angular frequency omega_k(eta) becomes uniquely temporally independent. Therefore any inertial observers embedded in a conformally flat FLRW spacetime all agree on the choice of virtual vacuum states. We postulate that the wavenumber k must be quantized in order to be able to regulate the vev by zeta regularization. Some fundamental implications of this result is derived, and likely conclusions drawn.