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)

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=1 P~10-3<<1

Intercommuting probability P

String gravity : conical structureThe 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.

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)]

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,

geodesic

potential

CMB lensing Deflection of CMB photons

Unlensed CMB map

[Hu+Okamoto(2002)]

z=zCMB

z=zL

z=0Lensed CMB map

Lensing contribution

“αβ-type” lensing bispectrum

The anisotropy is assumed to be decomposed into

(α,β : contributions from each components)

“αβ-type” lensing bispectrum

Various types of CMB lensing : contributions from cosmic strings

SP-type

PP-type (standard) PS-type

SS-type

Standard density pert.

Standard density pert.

Standard density pert.

Cosmic strings

Cosmic strings

Cosmic strings

Cosmic strings

Standard density pert.

“P” : primordial density perturbations, “S” : string contributions

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 ∝ Cl

ΘsφsClΘsΘs

∝(Gμ)4

(GKS)3

∝(Gμ)3

PreliminarySP-type

∝ ClΘsφsCl

ΘpΘp

∝(Gμ)2

PS-type ∝ Cl

ΘpφpClΘsΘs

∝ (Gμ)2

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

Constraint in Gμ-P plane ((S/N)<5000=1)

For small P, the PS-type GKS-L bispectrum C∝ lΘpφpCl

ΘsΘs (Gμ)∝ 2 gives the tighter constraint on Gμ than the (GKS)3 bispectrum (Gμ)∝ 3.

(GKS)3

PS-type ∝ Cl

ΘpφpClΘsΘs

SP-type ∝ Cl

ΘsφsClΘpΘp

[Yamauchi, KT, et al., in prep.]

PreliminarySS-type

∝ ClΘsφsCl

ΘsΘs

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.