Weak lensing from self-ordering scalar fields

Cosmological defects result from cosmological phase transitions in the early Universe and the dynamics reflects their symmetry-breaking mechanisms. These cosmological defects may be probed through weak lensing effects because they interact with ordinary matters only through the gravitational force. In this paper, we investigate global textures by using weak lensing curl and B modes. Non-topological textures are modeled by the non-linear sigma model (NLSM), and induce not only the scalar perturbation but also vector and tensor perturbations in the primordial plasma due to the nonlinearity in the anisotropic stress of scalar fields. We show angular power spectra of curl and B modes from both vector and tensor modes based on the NLSM. Furthermore, we give the analytic estimations for curl and B mode power spectra. The amplitude of weak lensing signals depends on a combined parameter $\epsilon^{2}_{v} = N^{-1}\left( v/m_{\rm pl} \right)^{4}$ where $N$ and $v$ are the number of the scalar fields and the vacuum expectation value, respectively. We discuss the detectability of the curl and B modes with several observation specifications. In the case of the CMB lensing observation without including the instrumental noise, we can reach $\epsilon_{v} \approx 2.7\times 10^{-6}$. This constraint is about 10 times stronger than the current one determined from the Planck. For the cosmic shear observation, we find that the signal-to-noise ratio depends on the mean redshift and the observing number of galaxies as $\propto z^{0.7}_{\rm m}$ and $\propto N^{0.2}_{\rm g}$, respectively. In the study of textures using cosmic shear observations, the mean redshift would be one of the key design parameters.