The constraints on the stochastic gravitational wave background from cosmic strings by an electromagnetic resonance system

TL;DR

This work proposes a GHz-band search for the stochastic gravitational wave background (SGWB) from cosmic strings using an electromagnetic (EM) resonance system that leverages the inverse Gertsenshtein effect in concert with a Gaussian beam. By employing analytic SGWB spectra across radiation, radiation-to-matter, and matter eras, including higher harmonics and relativistic-species suppression, the authors predict GHz-scale signal amplitudes and derive expected observables. A data-processing pipeline based on cross-correlation between two EM detectors, with an optimal filter and careful noise modeling (background EM, shot, and thermal noise), yields SNR estimates showing detectability for $G\mu \ge 10^{-11}$ at around 1 GHz (SNR ≳ 20) and much larger SNR for stronger strings, thereby establishing competitive GHz-band constraints. The results complement multi-band SGWB observations and set a foundation for future GHz-frequency GW searches, with suggested refinements including shielding, field optimization, and more accurate overlap reductions.

Abstract

As one of the primary detection targets for contemporary gravitational wave (GW) observatories, the stochastic gravitational wave background (SGWB) holds significant potential for enhancing our understanding of the early universe's formation and evolution. Studies indicate that the SGWB spectrum from cosmic strings can span an extraordinarily broad frequency range, extending from extremely low frequencies up to the microwave band. This work specifically investigates the detectability of cosmic string SGWB signals in an electromagnetic (EM) resonance system at GHz frequency. We present a systematic analysis encompassing: (1) the response of high frequency gravitational waves (HFGWs) in such EM resonance system. (2) the development and application of fundamental data processing protocols in the EM resonance system. Our results demonstrate that the EM system shows promising sensitivity to detect cosmic string SGWB signals with tension parameters $Gμ\geq 10^{-11}$ (the corresponding dimensionless amplitude $h \geq 10^{-33}$ at 1 GHz), while potentially establishing new constraints for $Gμ\leq 10^{-11}$ in the microwave band. These findings would complement existing multi-band SGWB observations and provide additional constraints on cosmic-string tension parameters in GHz frequency regimes.

Figures (7)

• Figure 1: The spectrum of the SGWB from cosmic string for $\alpha=0.1$, $\Gamma=50$, $n_*=10^{5}$, $q=4/3$, $g_*' = 106.75$, and $g_* = 3.36$, with different values of $G\mu$. The calculation is based on sousa2020fullwang2023probing and the theoretical framework presented in Section \ref{['sec:2']}.
• Figure 2: Structure of the EM Resonance System. The system is defined in a laboratory frame with x-y-z coordinate, which describes the physical configuration of Gaussian beam (GB), static magnetic field and microwave photon receivers. Specifically, GB from the transmitter propagates along z-axis towards +z direction. Static magnetic field pointing along the y-axis is localized in the region $-l_{1}\leq z\leq l_{1}$. Microwave photon receiver 1 positioned on the +x axis, detecting photons at its location, while microwave photon receiver 1' positioned on the -x axis, symmetrically opposite to receiver 1. The effective detection area of each receiver is given by $\Delta s=\Delta z\Delta y$.
• Figure 3: Left-panel: Schematic of a Gaussian beam propagating along the z-axis, showing the beam waist $W_{0}$ (minimum radius) and the Rayleigh range $z_{0}=\pi W^{2}_{0}/\lambda_{e}$. Right-panel: Normalized amplitude profile of the Gaussian beam versus frequency, centered at $f_{0} = 1 \times 10^9$ Hz. The bandwidth $\Delta f = 6.24$ MHz corresponds to the full width at half maximum (FWHM).
• Figure 4: Dimensionless amplitude of the SGWB from cosmic strings with different $G\mu$ in the GHz band. The calculation is based on Aggarwal2021, using the SGWB spectrum derived in Sect.\ref{['sec:2']}, with the detailed formulation provided in Sect.\ref{['subsec:3.2']}.
• Figure 5: (a)The PPFs of the SGWB from cosmic strings vary with $\phi$, here the number of $N^{(1)}_{x}$ is normalized. (b) The energy density spectrum of the PPFs generated by the SGWB from cosmic string in microwave frequency band. Here the related parameter values are consistent with those specified in Table \ref{['tab:1']}.