Scalar Field and Particle Dynamics in Conformal Frame

Abstract

The dynamics of the scalar field and particle in a conformal frame are considered. The conformal Klein-Gordon equation describing the scalar field is transformed into the quantum Telegraph equation in Minkowski space-time. The conformal factor acts like a background field having a perfect energy-momentum tensor. The scalar field decays exponentially with time during inflation allowing the conformal field to induce space energy. The conformal field grows with time at the expense of decreasing the energy density of the real scalar field. Einstein’s tensor embodies an energy-momentum tensor representing the background contribution reflecting the matter aspect of the gravitational field. The energy density arising from the conformal field is negative. The background energy associated with Einstein’s curvature tensor gives rise to massive gravitons that act like a cosmological constant. In an expanding Universe, this particular case yields a background energy proportional to the square of the scalar field mass giving rise to the massive graviton. Because of the background fluid, which is intrinsically coupled to space curvature, the particle’s motion is found to exhibit a drag force and therefore moves in a curved path even no matter around exists. It is found that breaking the conformal invariance gives rise to the mass generation of gravitons. PACS 04.20.-q, Classical general relativity; PACS 04.20.Cv, Fundamental problems and general formalism; PACS 95.30.Sf, Relativity and gravitation; PACS 4.62.+v, Quantum fields in curved space-time