Observing cosmic string loops with gravitational lensing surveys

We show that the existence of cosmic strings can be strongly constrained by the next generation of gravitational lensing surveys at radio frequencies. We focus on cosmic string loops, which simulations suggest would be far more numerous than long (horizon-sized) strings. Using simple models of the loop population and minimal assumptions about the lensing cross section per loop, we estimate the optical depth to lensing and show that extant radio surveys such as CLASS have already ruled out a portion of the cosmic string model parameter space. Future radio interferometers, such as LOFAR and especially SKA, may constrain $G\mu /c^2<{10}^{-9}$ in some regions of parameter space, outperforming current constraints from pulsar timing and the cosmic microwave backgound by up to two orders of magnitude. This method relies on direct detections of cosmic strings, and so is less sensitive to the theoretical uncertainties in string network evolution that weaken other constraints.

Figure 1

Regions of the $({\theta }_S,{\theta }_{\mathrm{loop}})$ parameter space where multiple images are formed by a planar circular loop. Regions are labeled depending on whether the $\pm$ Schwarzschild images are formed, or whether direct images of the source (S), are visible.

Figure 2

Contours for 10 and 100 expected events using the power-law loop spectrum model for CLASS/JVAS (C), LOFAR (L), and SKA (S), for a source population at redshift $z=1.2$. The $x$ axis is the power-law index $\gamma$ (see Sec. 2b1) and the $y$ axis is the density parameter in loops, ${\Omega }_{\mathrm{loop}}$. Ten expected events corresponds to a constraint at $3\sigma$ if no events are observed.

Figure 3

Contours for 10 and 100 expected events using the one-scale loop spectrum model for CLASS/JVAS (C), LOFAR (L), and SKA (S), for a source population at redshift $z=1.2$. We also plot the pulsar timing constraint from 45 (black dotted lines). The upper dotted line is for ${\Omega }_g{h}^2<2\times {10}^8$ and the lower is for ${\Omega }_g{h}^2<2\times {10}^9$—see 45 for a discussion of the uncertainty. In this plot, the $x$ axis is the one-scale model parameter $\alpha$ (see Sec. 2b2) and the $y$ axis is the dimensionless loop tension $G\mu /c^2$.