Constraining cosmic string parameters with curl mode of CMB lensing
  We present constraints on a cosmic string network with a measurement of weak
gravitational lensing from CMB temperature map. The cosmic string network
between observer and last scattering surface of CMB photons generates vector
and/or tensor metric perturbations, and the deflection of CMB photons by these
gravitational fields has curl mode which is not produced by the scalar metric
perturbations. In this paper, we use the power spectrum of curl mode obtained
from Planck to constrain the string tension, G\mu, and the reconnection
probability, P. In demonstrating the parameter constraints with Planck curl
mode, we also measure the lensing power spectrum from the Atacama Cosmology
Telescope (ACT) 2008 season data, which have better angular resolution with
lower instrumental noise on a much smaller chunk of the sky. Assuming P=1, the
upper bound on tension is G\mu = 6.6\times 10^{-5} with 2\sigma (95% C.L.),
using curl mode from Planck, which is weaker than that from the small-scale
temperature power spectrum. For small values of P, however, the constraint from
curl mode becomes tighter compared to that from temperature power spectrum. For
P\lsim 10^{-2}, we obtain the constraint on the combination of the string
parameters as G\mu P^{-1}\leq 3.4\times 10^{-5} at more than 2\sigma (95%
C.L.).
