Weak lensing generated by vector perturbations and detectability of cosmic strings

TL;DR

This paper investigates how vector perturbations from cosmic strings influence weak gravitational lensing signals, deriving formulas for observable effects, and assesses their detectability with upcoming measurements, potentially revealing cosmic string properties.

Contribution

It provides the first full-sky formulas for weak lensing signals caused by vector perturbations and evaluates their detectability from cosmic strings with upcoming surveys.

Findings

Weak lensing signals are enhanced for smaller intercommuting probabilities.

Potential detection of cosmic strings with tension down to Gμ ~ 5×10⁻⁸ for P ~ 0.1.

Detection of even smaller tensions, Gμ ~ 5×10⁻¹⁰, possible for P ~ 10⁻³.

Abstract

We study the observational signature of vector metric perturbations through the effect of weak gravitational lensing. In the presence of vector perturbations, the non-vanishing signals for B-mode cosmic shear and curl-mode deflection angle, which have never appeared in the case of scalar metric perturbations, naturally arise. Solving the geodesic and geodesic deviation equations, we drive the full-sky formulas for angular power spectra of weak lensing signals, and give the explicit expressions for E-/B-mode cosmic shear and gradient-/curl-mode deflection angle. As a possible source for seeding vector perturbations, we then consider a cosmic string network, and discuss its detectability from upcoming weak lensing and CMB measurements. Based on the formulas and a simple model for cosmic string network, we calculate the angular power spectra and expected signal-to-noise ratios for the B-mode cosmic shear and curl-mode deflection angle. We find that the weak lensing signals are enhanced for a smaller intercommuting probability of the string network, $P$, and they are potentially detectable from the upcoming cosmic shear and CMB lensing observations. For $P\sim 10^{-1}$, the minimum detectable tension of the cosmic string will be down to $G\mu\sim 5\times 10^{-8}$. With a theoretically inferred smallest value $P\sim 10^{-3}$, we could even detect the string with $G\mu\sim 5\times 10^{-10}$.