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

Abstract

A 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 $3d-1s$ transition of singly ionized helium ${\mathrm{He}}^{+}$, which gives a peak in frequency at $\sim 10^{13}$ 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 ${\mathrm{He}}^{+}$ 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.

14 pages, 1 figure, accepted for publication in Eur. Phys. J. C

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