We ask the question if an entropy S = E/T with a usual value ascribed of initial entropy S ~ 10⁵ of the onset of inflation can allow an order of magnitude resolution of the question of if there could be a survival of a graviton from a prior to the present universe, using typical Planckian peak temperature values of T ~ 10¹⁹ GeV. We obtain the values consistent with up to 1038 gravitons contributing to an energy value of E ~ 10²⁴ GeV if we assume a relic energy contribution based upon each graviton initially exhibiting a frequency spike of 1010 Hz. The value of E ~ 10²⁴ GeV is picked from looking at the aftermath of what happens if there exists a quantum bounce with a peak density value of ρ_maximum ~ 2.07 ρ_Planck as has been considered recently by P. Malkiewicz and W. Piechocki [15] in the LQG bounce regime radii of the order of magnitude of l ~ 10³⁵ meters. In this paper estimates specifically avoids using S = (E - μN)/T are done, by setting vanishing chemical potential μ = 0 for ultra high temperatures. Finally we compare briefly the obtained results with the ones recently investigated by G. 't Hooft [20] and L.A. Glinka [21, 22].