Gravitational Waves from High Temperature Strings

TL;DR

This paper investigates the gravitational wave signatures from high-temperature string gases in the early universe, revealing a potentially detectable spectrum that exceeds standard field theory predictions and relates directly to the string scale.

Contribution

It provides the first detailed calculation of gravitational wave spectra from long strings in the Hagedorn phase, highlighting their dominance over field theory signals and linking observables to the string scale.

Findings

Gravitational wave spectrum peaks at 50-100 GHz.

String signal amplitude exceeds standard model predictions.

Signal amplitude is proportional to the string scale $M_s$.

Abstract

We study finite temperature effects in string cosmology and their potential gravitational wave signature. Expanding on our recent work arXiv:2310.11494 , we consider a general configuration of highly excited open and closed strings at high enough temperature to be in the Hagedorn phase in 3+1 dimensions, in order to explore its cosmological implications. We find conditions, which can be satisfied in compactifications with moduli stabilization, that allow the long strings to remain in equilibrium in a controlled effective field theory, with equilibration driven by the joining and splitting of the dominant open string population. We calculate the emission rate of gravitons by long open strings, which we show is determined by ten dimensional flat space transition amplitudes available in the literature, and then find the total gravitational wave spectrum generated by the gas of long strings. The gravitational wave spectrum has robust characteristics. It peaks at frequencies of order 50-100 GHz, the same as for gravitational waves from the reheating epoch of the Standard Model. But the amplitude of the string signal is significantly larger than predicted by the Standard Model and its field theoretic extensions. The amplitude and other physical observables (such as the contribution to $\Delta N_{\text eff}$) are directly proportional to the string scale $M_s$; indicating that a potential signal may also determine the string scale. Our calculations provide one of the few examples of a signal of stringy origin that dominates over the field theory predictions. We give a physical explanation of our results and discuss further implications.