Do Gravitons from a Prior Universe Survive a LQG ‘Quantum Bounce’?

Abstract

We ask if a formula for entropy, as given by S ≡E/T with a usual value ascribed to initial entropy S~10⁵ at the onset of inflation allows an order of magnitude resolution of whether there could be a survival of a graviton from a prior to the present universe, during a ‘bounce’ as predicted by Loop Quantum Gravity, using typical Planckian peak temperature values of T~10¹⁹GeV. We obtain values consistent with up to 10³⁸ gravitons contributing to an energy value of E~10²⁴ GeV, if we assume a relic energy contribution where each graviton initially exhibits a frequency spike of 10¹⁰Hz. The value of E~10²⁴ GeV is picked from looking at the aftermath of what happens if there is a quantum bounce with a peak density value of ρ _{max imum} ~ 2.07·ρ_planck [16] in a regime of LQG bounce radii on the order of magnitude of λ~10^-35 meters. The author, in making estimates, specifically avoids using S≡[E-µN] by setting the chemical potential µ≡0 at ultra high temperatures – for reasons which are brought up in the conclusion.