Weak Lensing of CMB
by Cosmic Strings
and its Detectability
YAMAUCHI, Daisuke
Research Center for the Early Universe (RESCEU),
U. Tokyo
Based on the collaboration with T. Namikawa (Kyoto), A. Taruya (Kyoto),
Y. Sendouda (Hirosaki), K. Takahashi (Kumamoto)

Gravitational Lensing= method to ``see’’ invisibles

NASA/ESAWEAK LENSING observations can provide a direct evidence forthe intervening matter distributions along a line of sight by measuring
the spatial patterns of the deformation of the photon path. 2

Imaging survey
e.g. HSC, DES, LSST, Euclid…

Weak lensing measurement
CMB lensing
e.g. ACT, SPT, Planck, PolarBear,ACTPol, SPTPol, COrE,…

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Imaging survey
e.g. HSC, DES, LSST, Euclid…

Weak lensing measurement
CMB lensing
e.g. ACT, SPT, Planck, PolarBear,
ACTPol, SPTPol, COrE,…

4

CMB lensing
What we observe is a subtly distorted version ofthe primary CMB anisotropy.

Unlensed CMB map

Foreground
perturbations

Daisuke Yamauchi (RESCEU)

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Deflection field
The distortion effect of lensing on the primary CMB isexpressed by a remapping with the deflection angle “Δ”.

ΔnUnlensed:

Observed:
Daisuke Yamauchi (RESCEU)

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The two dimensional distortion vector Δ is decomposed
into gradient-mode: ∇φ and curl-mode: (*∇)ω .

(For details, see [DY+Namikawa+Taruya 1305.3348])

 Scalar metric perturbations at linear order produce only the gradient-mode,and the curl-mode can be induced by vector and/or tensor perturbations:

ScalarVector
TensorGradient-mode

Curl-modeTwo possible ways of detecting strings
from weak lensing of CMB

Gradient-mode

Curl-mode

String-inducedISW-lensing bispectrum

New probe
for cosmic strings

CURL-MODE
FROM COSMIC STRINGS
Curl-mode

Vector/tensor perturbations fromcosmic strings
Cosmic strings continuously generate vector and tensor metricperturbations even at late-time epoch, which induce the nonvanishing curl-mode signal at present time!
In order to compute the power spectrum analytically, we assume
several idealizations: Velocity dependent one-scale model for a string network[Martins+Shellard(1996,2002), Avgoustidis+Shellard(2006),…]

 Analytic model to estimate correlations within string segments[Hindmarsh(1994), Vincent+Hindmarsh+Sakellariadou(1997),Albrecht+Battye+Robinson(1999),…]

Vector/tensor perturbations fromcosmic strings
Cosmic strings continuously generate vector and tensor metricperturbations even at late-time epoch, which induce the nonvanishing curl-mode signal at present time!
Vector power spectrum[DY+Namikawa+Taruya 1305.3348]

Tensor power spectrum

(Full-sky curl-mode estimator [Namikawa+DY+Taruya 1110.1718])

Curl-deflection from cosmic strings[DY+Namikawa+Taruya, 1205.2139, 1305.3348]String tension Gμ =10-8
reconn. prob. P= 10-3

The curl-mode measurement would provide not only a directprobe of cosmic strings, but also a diagnosis helpful to check thesystematics in the derived constraints from the CMB TT. 12

Constraint on string parametersfrom curl mode for Planck curl-mode[Namikawa+DY+Taruya, 1308.6068](95%CL, Planck curl-mode)

String tension Gμ For P=1, Gμ<6.6×10-5
 Curl mode is more sensitive tosmall values of P compared tothe power spectrum.

Reconnection probability P13GRADIENT-MODE
FROM COSMIC STRINGS
Gradient-mode

ISW-lensing bispectrum A lensed fluctuation is a nonlinear function of fields

Lensing events lead to deviations from Gaussianity

 The cross-correlation due to the late-time evolution
induces the “ISW-lensing” bispectrum.

CMB lensing from primordial
perturbations (P) and cosmic strings (S)In the case of the various independent gravitational sources,
the observed CMB anisotropy can be regarded as a superpositionof those due to each source.

LensedForeground

UnlensedVarious types of CMB lensing“P” : Primordial density perturbations “S” : Cosmic strings PP-type (standard)Standard
Standard
density pert. density pert.

 SP-type
Standard
density pert.

 PS-typeCosmicstrings

Standard
density pert.

 SS-typeCosmicstrings

Cosmicstrings

Cosmicstrings

[DY+Sendouda+Takahashi, 1309.5528]

αβ-type ISW-lensing bispectrum: Primordial bispectrum: Primordial ISW-lensing [2σ detection, Planck19]

Cosmic strings: purely due to the GKS effect[Hindmarsh+(2009), Regan+Shellard(2010)]: String-induced GKS-lensing

[DY+Sendouda+Takahashi, 1309.5528]

Equilateral-shaped bispectra
induced by cosmic strings
SSS-type∝(Gμ)3SP-type∝(Gμ)2PS-type∝ (Gμ)2

Silkdamping(Gμ,P)(10-7,1)(10-8,10-3)(10-9,10-6)

 The standard ISW-L (PP-type) and SP-type bispectra are particularly
suppressed due to the Silk damping, so only the SSS- and PS-typebispectra are relevant at small scale.

[DY+Sendouda+Takahashi, 1309.5528]

Cumulative signal-to-noise ratio

Solid : Planck+ACTPol–like noise, dashed : Planck-like noise(Gμ,P)(10-7,1)(10-8,10-3)(10-9,10-6)

To estimate the feasibility to detect their signals, we quantify (S/N) in
the current and future CMB observations. The SP-type is not relevant,as expected.

[DY+Sendouda+Takahashi, 1309.5528]

Constraint in Gμ-P plane
Solid : Planck+ACTPol–like noise, dashed : Planck-like noise

SP-type ∝(Gμ)2

SSS-type∝(Gμ)3

CMB TT(P=1)[Planck25]

PS-type ∝(Gμ)2

For small P, the PS-type ISW-L bispectrum ∝ ClΘpφpClΘsΘs ∝ (Gμ)2 gives
the tighter constraint on Gμ than the SSS-type bispectrum ∝ (Gμ)3.

Summary Vector and tensor perturbations from cosmic strings induce
the non-vanishing curl-mode signal of the CMB lensing,which is potentially detectable for future observations.
 Cosmic strings are expected to cause weak lensing as well as
the ISW effect, which are naturally produces the yet anotherkind of the CMB temp. bispectra, string-induced ISW-lensing
bispectra (SP-, PS-, SS-type).

Thank you !

B-mode shear from cosmic strings[DY+Namikawa+Taruya, 1205.2139, 1305.3348]
Fiducial string parameters : String tension Gμ =10-8, reconnection prob. P= 10 -3

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APPENDIXClΘsΘs and ClΘsφs

Gμ-P dependence
 GKS-induced power spectrum

ClGKS ~ (GKS amplitude)2 × (string number)∝ 1/(correlation length)3~ (Gμ)2~ P-3/2
 Curl-mode power spectrum~ (Gμ)2~ P-3/2
Clcurl ~ (amplitude)2 × (string number)× (energy density per single segment)∝ 1/(correlation length)2~ P-1