High-frequency Gravitational Waves from Superstring Phases in the Early Universe

TL;DR

This work proposes that in the early universe moduli dynamics can drive a novel string loop tracker, where time-varying string tension concentrates energy into loops that grow in size while evading evaporation. The decay of these loops during a modulus-dominated epoch generates a high-frequency stochastic gravitational-wave background, with a peak in the GHz range today whose amplitude is highly sensitive to the duration of modulus domination and the modulus decay mechanism. Within the Large Volume Scenario (LVS), canonical (gravitational) decays yield long moduli-dominated periods and highly diluted signals, while fast-decaying or non-gravitational decays can significantly boost the peak, potentially placing it near $f^{\rm obs}_{\rm peak}\sim 10^{8}-10^{10}$ Hz and $\Omega^0_{\rm GW,peak}$ in the $10^{-7}$ to $10^{-11}$ range for plausible compactification volumes. The study highlights high-frequency gravitational waves as a potential, though challenging, observational window into string cosmology, and outlines future directions including relaxing the isolated-loop assumption and exploring broader loop-size distributions.

Abstract

When moduli roll in the early universe, all physical scales - including string tensions - simultaneously evolve. The dynamics of cosmic string loops with time-varying tension can produce cosmic string loop trackers in which most of the energy density of the universe lies in the form of string loops. This solution can exist as an attractor until the rolling modulus reaches its minimum, when the loops ultimately decay through gravitational wave emission. We explore the spectrum of gravitational waves produced by such string loop trackers. The resulting spectrum is high-frequency and peaks in the GHz regime today. The amplitude of the signal is diluted by any subsequent matter-dominated epochs, and thus the potential observability of the signal crucially depends on the duration of the moduli-dominated epoch that follows once the moduli settle down and oscillate about their minimum.

Figures (2)

• Figure 1: Different phases of the evolution of the system we consider, which ultimately leads to a stochastic background of gravitational waves (yellow sinusoidal waves) that were emitted by cosmic string loops (red) as the modulus (grey ball) evolves towards the minimum of its potential (blue). The numbers refer to the epochs discussed in Section \ref{['summarysec']}.
• Figure 2: Gravitational power spectrum from a population of loops emitting while the volume modulus is oscillating about its minimum. The coloured lines correspond to emission in the context of LVS and a fast modulus decay rate $\Gamma_\phi \simeq (1/4\pi)^2(M_P/m_\phi)^{4/3} \cdot m_\phi^3/ M_P^2$. The dashed line represents the best case scenario, realised in the case of modulus decay via non-gravitational couplings, allowing for the time of reheating $t_{\rm rh}$ to occur at the end of the lifetime of the loops $\tau$. In the plot, this is shown for a volume in string units of $\mathcal{V}=10^{10}$ with $\Omega_{\rm loops}^{\rm i}$ taken such that the peak saturates the BBN constraint. The initial size of the loops is taken to be $\varepsilon=\sqrt{G\mu}$.