Reference Introduction Polarization Observation Summary

B-mode Polarization of The Cosmic

Microwave Background

Yuri Hayashida

May 27, 2015

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Reference Introduction Polarization Observation Summary

Index

Reference

Introduction

Polarization

Observation

Summary

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Reference Introduction Polarization Observation Summary

Reference

[1] Baumann,D. (2012). ”TASI Lectures on Inflation”, arXiv:0907.5424.

[2] Carlisle, M.C.(2014). Sky and Telescope.“Direct Evidence of Big Bang

Inflation”. http://www.skyandtelescope.com/astronomy-news/

direct-evidence-of-big-bang-inflation/ (accesed 2015-05-18)

[3] The BICEP2/Keck and Planck Collaborations, Phys. Rev. Lett. 114, 101301,

2015

[4] The BICEP2 Collaboration, Phys. Rev. Lett. 112, 241101, 2014

[5] Planck Collaboration. (2014). arXiv:1409.5738v2 [astro-ph.CO]

[6] Planck Collaboration. (2015). arXiv:1502.02114v1 [astro-ph.CO]

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Reference Introduction Polarization Observation Summary

Cosmic Microwave Background

What is the CMB?

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Inflation

What is the inflation?

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Reference Introduction Polarization Observation Summary

Powerspectrum of the Tensor Perturbation

The powerspectrum of the tensor perturbation, ∆2t , gives the

energy scale of the inflation directly.

∆2t =

2

π2

H2

M2pl

(1)

If we assume slow-roll inflation model,

∆2t ∝ H2 ≈ V, (2)

where V is the infraton potential.

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Reference Introduction Polarization Observation Summary

Gravitational Wave

In the early universe, there were primordial gravitational waves.

ds2 = −dt2 + a2(t)∑ij

[δij + hij(t, x

i)]dxidxj (3)

� �1. Gravitational waves are transverse.

2. Gravitational waves have two polarization srates.

3. Gravitational waves are spin-2.

Therefore, hij is a rank-2 tensor field.� �7 / 19

Reference Introduction Polarization Observation Summary

Thomson ScatteringThe polarization is generated by Thomson scattering.

Credit: Leah Tiscione / Sky & Telescope[2]

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Reference Introduction Polarization Observation Summary

Polarization

Stokes Palameter: Q,U

(Q± iU)(n̂) =∑l,m

a±2,lm±2Ylm(n̂) (4)

where n̂ denotes direction of the sky, and ±2Ylm is tensor

spherical harmonics.

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Reference Introduction Polarization Observation Summary

Polarization

the linear combination

αE,lm ≡ −1

2(a2,lm + a−2,lm) , αB,lm ≡ −

1

2i(a2,lm − a−2,lm)

(5)

two scalor fields

E(n̂) =∑l,m

aE,lmYlm(n̂), B(n̂) =∑l,m

aB,lmYlm(n̂) (6)

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Reference Introduction Polarization Observation Summary

Polarization modesE-mode ← scalor and tensor perturbation

B-mode ← tensor (and vector) perturbation

Two modes of polarization[1]

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Reference Introduction Polarization Observation Summary

Why is B-mode so important?

B-mode polarization of CMB is just a good evidenceof the inflation. Moreover, it has some cosmologicalimformation.

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Reference Introduction Polarization Observation Summary

BICEP2In Mar 2014, BICEP2 group announced that they detected

B-mode polarization generated by primordial gravitational

waves.[4]

BICEP2 team [4]

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Reference Introduction Polarization Observation Summary

BICEP2“BICEP2 was a specialized, low angular resolution experiment

which operated from the South Pole from 2010 to 2012.”[3]

Planck Collaboration(2014)[5]

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BICEP2

BICEP2(2014)[4]

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Detection...?

“ Taking cross spectra against 100 GHz maps from BICEP1

we find significant correlation and set a constraint on the

spectral index of the B-mode excess consistent with CMB and

disfavoring dust by 1.7σ. “[4]

⇓... In Feb 2015, BICEP2/Keck, Planck Collaborations reported

that ”We find strong evidence for dust and no statistically

significant evidence for tensor modes.”[3]

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Reference Introduction Polarization Observation Summary

Detection...?

“ Taking cross spectra against 100 GHz maps from BICEP1

we find significant correlation and set a constraint on the

spectral index of the B-mode excess consistent with CMB and

disfavoring dust by 1.7σ. “[4]

⇓... In Feb 2015, BICEP2/Keck, Planck Collaborations reported

that ”We find strong evidence for dust and no statistically

significant evidence for tensor modes.”[3]

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Reference Introduction Polarization Observation Summary

Constraints: Planck results 2015The constraint on the tensor-to-scalor ratio (Planck 2015 [6])

r ≡ ∆2t

∆2s

(7)

Planck 2015[6]

The energy scale of the inflaion

V 1/4⋆ = (1.88× 1016 GeV)

( r

0.10

)1/4

(8)

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Reference Introduction Polarization Observation Summary

Constraints: Planck results 2015

Planck(2015)[6]

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Summary

▶ The B-mode polarization on large scales is generated by

the primordial gravitational waves.

▶ The B-mode polarization is a good evidence of the

inflation and has some information about the early

universe.

▶ This B-mode polarization have not yet detedted.

▶ The tensor-to-scalor ratio, r, is constrained

r0.002 < 0.10 (95% CL, Planck TT+lowP)[6].

▶ Its constraint gives the energy potential of inflation:

V1/4⋆ = (1.88× 1016 GeV)

(r

0.10

)1/4.

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