1. CMB temperature bispectrum from a cosmic string network Keitaro Takahashi (Kumamoto U) Based on the collaboration with Yamauchi (U Tokyo), Sendouda (Hirosaki U), Yoo (Nagoya), Hiramatsu (Kyoto)

2.  Line-like topological defects  Formed in the early universe through the spontaneous symmetry breaking  F-strings, D-strings, and their bound states which appear in string theory  Formed though the brane collision at the end of the stringy inflation Cosmic strings Cosmic superstrings P=1P~10 -3 <<1  Intercommuting probability P

3. String gravity : conical structure The spacetime around a straight cosmic string is locally flat. An angular wedge of width Δ=8πGμ is removed from the space and the remaining edges identified.

4. String-induced integrated Sachs-Wolfe effect [Planck 25 (2013)] (δT/T)/Gμ Cosmic strings create line-like discontinuities in the CMB signal. Gott-Kaiser-Stebbins (GKS) effect [Kaiser+Stebbins(1984), Gott III(1985)]

5. CMB temp. power spectrum induced by a cosmic string network An analytic model including the probabilistic nature of the intercomuting process [Yamauchi, KT, et al. (2011)] [Atacama Cosmology Telescope (ACT), 2010] For ACT, For Planck satellite,

6. geodesic potential CMB lensing  Deflection of CMB photons Unlensed CMB map [Hu+Okamoto(2002)] z=z CMB z=z L z=0 Lensed CMB map Lensing contribution

7. “αβ-type” lensing bispectrum  The anisotropy is assumed to be decomposed into (α,β : contributions from each components) “αβ-type”  “αβ-type” lensing bispectrum

8. Various types of CMB lensing : contributions from cosmic strings SP-type PP-type (standard) PS-type SS-type Standard density pert. Cosmic strings Standard density pert. “P” : primordial density perturbations, “S” : string contributions

9. Equilateral-shaped bispectra induced by a cosmic string network Silk damping  At small scale, the standard ISW-L (PP-type) and SP-type bispectra are damped due to the Silk damping, and only the (GKS) 3, PS-type bispectra are relevant. (Gμ,P) (10 -7,1) (10 -8,10 -3 ) (10 -9,10 -6 ) [Yamauchi, KT, et al., in prep.] SS-type ∝ C l Θsφs C l ΘsΘs ∝ (Gμ) 4 (GKS) 3 ∝ (Gμ) 3 Preliminary SP-type ∝ C l Θsφs C l ΘpΘp ∝ (Gμ) 2 PS-type ∝ C l Θpφp C l ΘsΘs ∝ (Gμ) 2

10. Cumulative signal-to-noise ratio (GKS) 3 ∝ (Gμ) 3 SS-type ∝ (Gμ) 4 PS-type ∝ (Gμ) 2 SP-type ∝ (Gμ) 2 PA : Planck+ACTPol–like noise, P : Planck-like noise [Yamauchi, KT, et al., in prep.] Preliminary

11. Constraint in Gμ-P plane ((S/N) <5000 =1) For small P, the PS-type GKS-L bispectrum ∝ C l Θpφp C l ΘsΘs ∝ (Gμ) 2 gives the tighter constraint on Gμ than the (GKS) 3 bispectrum ∝ (Gμ) 3. (GKS) 3 PS-type ∝ C l Θpφp C l ΘsΘs SP-type ∝ C l Θsφs C l ΘpΘp [Yamauchi, KT, et al., in prep.] Preliminary SS-type ∝ C l Θsφs C l ΘsΘs

12. Summary  We study the effect of weak lensing by cosmic strings on the anisotropies of cosmic microwave background.  In developing a method to evaluate the lensing contribution due to strings, we calculate the analytic expression for the various-type, namely αβ-type, lensing bispectra.  For smaller tension, the lensing bispectrum have window to constrain the string parameters even tighter than the bispectrum induced by GKS.