On the observation of cosmic strings via gravitational-wave lensing

TL;DR

This paper develops a dedicated framework to detect gravitational-wave lensing by cosmic strings, using a full-wave transmission factor F(f) expressed analytically through Fresnel integrals to capture diffraction and interference from conical spacetime. It establishes how CS lensing differs fundamentally from point-mass lensing, with two identical, non-amplified images and a distance-dependent wave effect that yields characteristic beating and time-delayed replicas in BBH signals. The authors quantify observability, biases in unlensed template searches, and the ability to distinguish CS lensing from PML and unlensed scenarios through Bayesian model selection, showing CS signatures are detectable and separable across broad parameter ranges. The framework enables efficient template generation for LVK pipelines and paves the way for using GW lensing as a probe of high-energy physics and early-Universe cosmology.

Abstract

We present a framework for detecting gravitational-wave signals lensed by cosmic strings (CSs), addressing a key gap in current searches. CSs, whose detection would provide a unique probe of high-energy physics and the early Universe, possess distinct topological and geometric features that require a dedicated search strategy. Our approach employs a full-wave transmission factor, expressed analytically via Fresnel integrals, which captures the characteristic diffraction and interference effects of the conical spacetime around a straight CS. We contrast CS lensing with the well-studied point mass lens (PML) model, highlighting their fundamental differences: CS lensing depends on cosmological distances, string tension $Δ$, and wavelength $λ$, and produces two non-amplified images set by the global conical geometry. In contrast, PML lensing is governed by the distance-independent ratio $\sim M_{Lz}/λ$, where $M_{Lz}$ represents the redshifted mass of the lens, with image properties derived from the lens equation. For BBH mergers lensed by CSs, we show that the waveforms exhibit a characteristic beating pattern or time-separated, exact replicas. We derive a detectability bound on the string tension and, using Bayesian model selection, demonstrate that CS lensing is distinguishable from both unlensed and PML-lensed signals across a wide region of parameter space.

Figures (11)

• Figure 1: Schematic diagram illustrating wave propagation in a conical space at the $z=0$ plane: (a) The source $S$ emits a GW. Two representative geodesics (depicted in red) pass on opposite sides of the string $L$ and are deflected by the angle $\Delta$; (b) An equivalent space with a deficit angle of $2\Delta$ and two image sources, $S^-$ and $S^+$. The geodesics are straight lines in this configuration.
• Figure 2: Density plot of the transmission factor $|F|$ for a cosmic string lens as a function of the rescaled frequency $ft_{\Delta}$ and source position $y=\theta/\Delta$. The dashed lines mark the boundary of the double-imaging region ($|y|<1$).
• Figure 3: Approximations to the transmission factor $|F|$ from Fig. \ref{['fig:F-string-full']}: (a) geometrical optics (GO); (b) geometrical theory of diffraction (GTD), which extends GO by including an additional diffracted contribution [Eq. \ref{['eq:F-GTD']}].
• Figure 4: Density plot of the transmission factor $|F|$ for a point-mass lens, shown as a function of the rescaled frequency $ft_M$ and source position $y = \theta / \theta_{\rm E}$. See Ref. BU-JCAP-21 for details.
• Figure 5: Transmission factor $|F|$ as a function of frequency for a source aligned with the line of sight ($y = 0$), showing the effect of varying the string tension $\Delta$ (and the corresponding lensing time delay $t_{\Delta}$). The LVK detectability band is indicated by the black dashed lines, ranging from $15\,$Hz to $500\,$Hz for illustration.