High frequency background gravitational waves from spontaneous emission of gravitons by hydrogen and helium

Abstract

AbstractA direct consequence of quantization of gravity would be the existence of gravitons. Therefore, spontaneous transition of an atom from an excited state to a lower-lying energy state accompanied with the emission of a graviton is expected. In this paper, we take the gravitons emitted by hydrogen and helium in the Universe after recombination as a possible source of high frequency background gravitational waves, and calculate the energy density spectrum. Explicit calculations show that the most prominent contribution comes from the $$3d-1s$$ 3 d - 1 s transition of singly ionized helium $$\mathrm {He}^{+}$$ He + , which gives a peak in frequency at $$\sim 10^{13}$$ ∼ 10 13 Hz. Although the corresponding energy density is too small to be detected even with state-of-the-art technology today, we believe that the spontaneous emission of $$\mathrm {He}^{+}$$ He + is a natural source of high frequency gravitational waves, since it is a direct consequence if we accept that the basic quantum principles we are already familiar with apply as well to a quantum theory of gravity.