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

TL;DR

This paper explores the theoretical prediction that spontaneous graviton emission from hydrogen and helium atoms after recombination could produce a high frequency gravitational wave background, with the most significant contribution from helium ion transitions.

Contribution

It provides the first detailed calculation of the energy density spectrum of high frequency gravitational waves from atomic graviton emission, highlighting helium ion transitions as a key source.

Findings

Peak frequency around 10^{13} Hz from helium ion transitions.

Energy density too small for current detection capabilities.

Confirms spontaneous graviton emission as a natural consequence of quantum gravity principles.

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 $\sim10^{13}$ 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.