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 \raise 2.9 pt \hbox { $ \scriptstyle < $ } \hskip { -6.0 pt } \lower 0.5 pt \hbox { $% \scriptscriptstyle \sim$ } 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 .
) .