Creation of quantized particles, gravitons and scalar perturbations by the expanding universe

Quantum creation processes during the very rapid early expansion of the universe are believed to give rise to temperature anisotropies and polarization patterns in the CMB radiation. These have been observed by satellites such as COBE, WMAP, and PLANCK, and by bolometric instruments placed near the South Pole by the BICEP collaborations. The expected temperature anisotropies are well-confirmed. The B-mode polarization patterns in the CMB are currently under measurement jointly by the PLANCK and BICEP groups to determine the extent to which the B-modes can be attributed to gravitational waves from the creation of gravitons in the earliest universe. It was during 1962 that I proved that quanta of the minimally-coupled scalar field were created by the general expanding FLRW universe. This was relevant also to the creation of quantized perturbations of the gravitational field, since these perturbations satisfied linear field equations that could be quantized in the same way as the minimally-coupled scalar field equation. In fact, in 1946, E.M. Lifshitz had considered the classical Einstein gravitational field in FLRW expanding universes and had shown that the classical linearized Einstein field equations reduced, in what is now known as the Lifshitz gauge, to two separate classical minimally-coupled massless scalar field equations. These field equations of Lifshitz, when quantized, correspond to the field equations for massless gravitons, one equation for each of the two independent polarization components of the spin-2 massless graviton. I will discuss this further in this article.1 1 Plenary Lecture given September 2, 2014 at the ERE2014 Conference in Valencia, Spain