Detecting Cosmic Strings with Lensed Fast Radio Bursts

Correlated red noise recently reported from pulsar timing observations may be an indication of stochastic gravitational waves emitted by cosmic strings that formed during a primordial phase transition near the Grand Unification energy scale. Unfortunately, known probes of cosmic strings, namely the Cosmic Microwave Background anisotropies and string lensing of extragalactic galaxies, are not sensitive enough for low string tensions of $G\mu = 10^{-10}-10^{-7}$ that are needed to explain this putative signal. We show that strong gravitational lensing of Fast Radio Bursts (FRBs) by cosmic strings is a potentially unambiguous avenue to probe that range of string tension values. The image pair of string lensing are expected to have identical magnification factor and parity, and have a typical time delay of $\sim 10^2\,\,(G\,\mu/10^{-8})^2$ seconds. The unique spectral fingerprint of each FRB, as well as the possibility to detect correlations in the time series of the electric field of the radio waves, will enable verification of the string lensing interpretation. Very-Long-Baseline Interferometry (VLBI) observations can spatially resolve the image pair and provide a lower bound on the string tension based on the image separation. We calculate the FRB lensing rate as a function of FRB detection number for several different models of the FRB redshift distribution. We find that a survey detecting $\sim 10^5$ FRBs, in line with estimates for the detection rate of the forthcoming survey CHORD, can uncover a strong lensing event for a string tension of $G\mu \simeq 10^{-7}$. Larger FRB surveys, such as Phase 2 of the Square Kilometre Array (SKA), have the potential to significantly improve the sensitivity on the string tension to $G\mu \simeq 10^{-9}$.