Graviton emission by a thermal bath of photons

The rate of emission of gravitons by a thermal bath of protons is calculated. Linearized quantum gravity is used to find the rate of graviton creation by thermal fluctuations of the photons. For the case of photons confined within a sphere of radius R and volume V at temperature T, the power radiated in gravitons is found to be P=(2.7×${10}^{\mathrm{-}66}$ erg/s)(V/${\mathrm{cm}}^3$)(T/K${)}^7$ln(160RT/K/cm). If the thermal bath cools solely by emission of gravitons, the cooling time is of the order of τ=(3×${10}^{51}$ s) (1 K/T${)}^3$ln(160RT/K cm). Any region which has been cooling by graviton emission since the early Universe has a maximum temperature of 10 MeV at the present.