SKAによる再電離時の21CM線観測を⽤いた
宇宙論パラメータの精密測定
Yoshihiko Oyama
ICRR

1 /44

◇ 宇宙論における21cm線観測の利⽤
𝝀𝟐𝟏 = 21 cm

物質分布（密度揺らぎ）の情報を持つ宇宙論パラメータ （Ω#$% 等） を制限できる(CMB観測のように)
M.McQuinn, O.Zahn, M.Zaldarriaga, L.Hernquist, S.R.
Furlanetto(2006) Astrophys.J.653:815-830,2006

2 /44

◇ 宇宙論における21cm線観測の利⽤
今回は以下の内容について話します◆ ニュートリノ質量

Y. Oyama, K. Kohri, M. Hazumi,
JCAP 1602, no. 02, 008 (2016).

◆ Dark energyのEOS

K. Kohri, Y. Oyama, T. Sekiguchi,T. Takahashi, arXiv:1608.01601.

◆ 素粒⼦論モデルの制限・軽いグラビティーノ
dark matterの質量
他にもY. Oyama, M. Kawasaki,arXiv:1605.09191.

ゆらぎのスケール依存性, ⾮ガウス性などの決定に有効である可能性が指摘されている

3 /44

◆ Contents
1. 21cm線観測の概要
2. SKA等の将来の21cm線観測による宇宙論モデルの制限(1) ニュートリノ質量(2) Dark energy(3) 軽いグラビティーノdark matter4 /44

◆ Contents
1. 21cm線観測の概要
2. SKA等の将来の21cm線観測による宇宙論モデルの制限(1) ニュートリノ質量(2) Dark energy(3) 軽いグラビティーノdark matter
5 /44

◇ 21cm線
中性⽔素原⼦の超微細構造が起源の電波◆陽⼦・電⼦のスピン・スピン相互作⽤に起因
超微細構造
1S state

全スピン=1triplet

𝜆 = 21cm

全スピン=0singlet

𝜈78 = 1.42GHz

𝛥𝐸 = 5.8×1023 eV

protonelectron

6 /44

◇ 観測対象：Cosmic dawn–再電離
Dark age Cosmic dawn 再電離(reionization)

SKAの観測範囲

Lunar array

21cm線吸収線※ 下段のグラフは輝度温度

21cm線放射線7 /44

J. R. Pritchard and A. Loeb◇ 21cm線観測の利点
Z=0linearnon linear

𝑃(𝑘) [ℎ2G Mpc G ]𝑃(𝑘) [ℎ2G Mpc G ]１. high z ほど密度揺らぎの⾮線形性が⼩さい

𝑘 [ℎ Mpc 28 ]Z=3linearnon linear
𝑘 [ℎ Mpc 28 ]２.広い⾚⽅偏移の範囲の観測
独⽴な波数のmode + 密度揺らぎの時間発展

8 /44

◇ 21cm線輝度温度： Δ𝑇O ≡ 𝑇O − 𝑇#%X
Δ𝑇O

𝜈78, 𝒓, 𝑧 ≈ 27𝑥KL 1 + 𝛿O1+𝑧

ΩO ℎ70.023

𝑇#%XFluctuation of baryon × 1 −𝑇Y𝑻𝒃 : Brightness tempof 21 cm line
𝑻𝑺 : Spin temp
𝑻𝐂𝐌𝐁 : CMB temp
𝑥KL : Neutral fraction

80.15 1 + 𝑧 7

ΩQ ℎ7 10𝐻(𝑧)/(1 + 𝑧)
mk𝑑𝑣|| /𝑑𝑟||𝑻𝑺 > 𝑻𝐂𝐌𝐁 emission（6 ≲ z ≲ 15）
𝑻𝑺 < 𝑻𝑪𝑴𝑩 absorption（15 ≲ z ）9 /44

Spin temperature : 𝑻𝑺Definition of 𝑇Y :

𝑛8 𝑔8
ℎ𝜈78
≡ exp −𝑛p 𝑔p𝑘t 𝑇Y

𝑛8 , 𝑛p : number density of spin 1, 0 state
𝑇Y depends on the following,(1) H-H, H-e, H-p collision(2) CMB photon(3) Lyα photon(4) Variation of neutral fraction 𝑥uv𝑥uv ≡ 𝑛uv ⁄𝑛u10 /44

スピン温度の従う方程式
𝜕 𝑇z{|𝜕𝑡 𝑇}

１ 𝜕𝑛p １ 𝜕𝑛8=
−𝑛p 𝜕𝑡𝑛8 𝜕𝑡ℎ𝜈78
𝑇Y , 𝑇• , 𝑇€ , 𝑇#%X ≳ 𝑇#%Xp ≈ 2.7𝐾 ≫ 𝑇z{| ≡= 0.068K𝑘t

𝜕 1𝜕𝑡 𝑇}

=4𝐶8p

1
1−
𝑇• 𝑇}

+ 𝑃8p

collision

11𝑇#%X 11−+ 𝐴8p−𝑇€ 𝑇}
𝑇z{| 𝑇‚ 𝑇}

LyαCMB Photon

1 𝜕𝑥uv 1−𝑥uv 𝜕𝑡 𝑇}

𝑥uv の時間変化

2017/1/81111/44

平衡状態のスピン温度
𝜕 1𝜕𝑡 𝑇}

≈ 0,𝜕𝑥uv≈0
𝜕𝑡𝑇#%X + 𝑦‰ 𝑇• +𝑦€ 𝑇€
𝑇Y =1 + 𝑦‰ + 𝑦€
𝐶8p 𝑇78𝑦‰ ≡𝐴8p 𝑇•𝑦‰ ≫ 𝑦€ , 1
𝑇Y ≈ 𝑇•𝑃8p 𝑇78𝑦€ ≡𝐴8p 𝑇€ℎ𝜈78
𝑇z{| ≡𝑘t𝑦€ ≫ 𝑦‰ , 1

1 ≫ 𝑦‰ , 𝑦€

𝑇Y ≈ 𝑇€

𝑇Y ≈ 𝑇#%X 12 /44

𝑇Y at the reionization
𝟏𝟎 ≲ 𝐳 < 𝟐𝟎10G𝑇•

T[K]

107

10𝑻𝜸 ∝ 𝒂2𝟏𝑻𝐠𝐚𝐬 ∝ 𝒂2𝟐

X-ray heating
z=10zz=20

Brightness temp
near z ~ 10

X-ray heating

𝑻𝑺 ≈ 𝑻𝐠𝐚𝐬 ≫ 𝑻𝜸Lyα(from stars)
Δ𝑇O ∝ 1 −“”“•13 /44

21cm line fluctuation 𝛿78
Δ𝑇O–O} − Δ𝑇O–O}
𝛿78 ≡Δ𝑇—O–O}

𝑇Y ≫ 𝑇‚ ：z~10

Neutral Peculiar ≡ 1 + 𝑧 𝑑v ||Baryon fraction velocity 𝐻(𝑧) 𝑑𝑟

𝜹𝟐𝟏 ≈ 𝜹™ + 𝜹𝒙𝐇𝐈 −𝜹𝝏𝒗
Fourier component (linear)𝟐¡¡𝟐𝟏 ≈ 𝜹¡𝐛 + 𝜹
¡𝐇𝐈 + 𝝁 𝜹𝐛𝜹¥||𝜇 ≡ |𝒌|Redshift space distortion

14 14/44

Power spectram of 21cm 𝑃78 (𝑘, 𝜇)∗𝛿§78 (𝒌)𝛿§78(𝒌’) ≡ 2𝜋 G 𝛿 « (𝒌 − 𝒌′) 𝑃78 (𝑘, 𝜇)–O} 7—𝑃“® ≡ Δ𝑇O𝑃787–O}
7—= Δ𝑇O /𝑥̅KL ° 𝑥̅KL𝑃±± − 2𝑥̅KL 𝑃²± + 𝑃²²
77+2𝜇7 𝑥̅KL𝑃±± − 𝑥̅KL 𝑃²± + 𝜇³ 𝑥̅KL𝑃±± ´

𝑃±± : Matter power spectrum
𝑃²± = 𝑥̅- 𝑃±µ ±: Density-ionization power spectrum

𝑃²² = 𝑥̅-7 𝑃±µ ±µ: Ionization power spectrum

Ionization fraction : 𝑥- = 1 − 𝑥KL

1515/44◆ Contents
1. 21cm線観測の概要
2. SKA等の将来の21cm線観測による宇宙論モデルの制限(1) ニュートリノ質量(2) Dark energy(3) 軽いグラビティーノdark matter

3. Summary

16 /44

◆ Constraints on the neutrino mass
Y. Oyama, K. Kohri, M. Hazumi,
JCAP 1602, no. 02, 008 (2016).

17 /44

◇ Growth of the density fluctuation 𝛿Q
Large scale ( > Free streaming scale)ΩQ = Ω¶«· + ΩO + Ωz
All components contribute the growth𝜹𝒎of ∝ 𝒂.
Small scale ( < Free streaming scale)ΩQ = Ω¶«· + ΩO + Ωz
Neutrino does not contributes the growth of 𝜹𝒎 .
𝟑𝟏2 𝒇𝝂𝜹𝒎 ∝ 𝒂 𝟓 ,𝝆𝝂𝒇𝝂 ≡𝝆𝒎

18 /44

Matter power spectrum 𝑷 𝒌 = 𝜹𝒌 𝟐
𝒁=𝟎Suppression
due to thefreestreamingTotal mass Σ𝑚z = 𝑚8 + 𝑚7 + 𝑚G .
(Here, 𝑚8 = 𝑚7 = 𝑚G ). ΩQ ℎ7 is fixed.

19/44

◆ Analysis methods

20 /44

Fisher Information matrix 𝑭𝒊𝒋𝜕 7 ln 𝐿(𝜽|𝒙)𝐹€Ã ≡𝜕𝜃€ 𝜕𝜃Ã𝐿(𝜽|𝒙):Likelihoodfunction𝜃€Ã :theoretical parameters

𝒙:data vector

Cramé r-Rao boundÊ ) ≥ 𝐹 28 €Ã𝑉€Ã (𝜽Ê )：variance of 𝜃Ì𝑉€Ã (𝜽We can estimate minimum variance of 𝜃Ì.
21 /44

Fisher matrix of 21 cm line observations
M.McQuinn et. al, Astrophys.J.653:815-830,2006

𝜕𝑃“® (𝒖- ) 𝜕𝑃“® (𝒖- )𝐹€Ã = Ñ7𝜕𝜃€𝜕𝜃Ã𝛿𝑃(𝒖)“®
121cm line power spectra : 𝑃“® (𝒖- ) ≡ 𝛿𝑇—O 7 𝑃78 (𝒖- )𝜆7 𝑇}Ø}Detector Noise： 𝑃Ó–-}Ô (𝑢Ö ) ≡ 𝐴
Ô71𝑛O (𝑢Ö )𝑡p8/7

𝛿𝑃“® (𝒖- ) ≡ (𝑃“® (𝒖- ) + 𝑃Ó–-}Ô (𝑢Ö,- ))/(𝑁‰ )𝒖 = 𝒖Ö , 𝑢∥ = (𝑑Ú (𝑧)𝒌Ö , 𝑦(𝑧)𝑘∥ )𝑑Ú (𝑧)：commoving angular diameter distance𝑦 𝑧 = 𝜆78 1 + 𝑧 /𝐻(𝑧)22 /44◇ CMB polarization experiments◆ POLARBEAR-295, 150 GHz◆ Simons Array

POLARBEAR-2 × 395, 150, 220 GHz

KEK CMB group is developing these experiments.

We took account of combinations ofabove 2 experiments and Planck satellite.

23 /44◇ 21cm line experiment◆ SKA (Square kilometer Array)
SKA low frequency(Australia)
Construction of Phase1
will start in 2018.

http://www.skatelescope.org/

SKA 1 は re-baseline後のスペックを想定

SKA 2 は re-baseline前のSKA1の集光⾯積の4 倍（当初のスペック）
24 /44

◆ Constraints on the neutrino total massand effective number of neutrino species 𝑵𝝂

Planck +POLARBEAR 2 + DESI

𝑵𝝂Planck +Simons Array + DESI+ SKA pahse1+ SKA phase 2Planck

95% C.L. expectedcontours
𝜮𝒎𝝂 = 𝟎. 𝟏eV
The neutrino total
mass is detectable
at 95%C.L.,
by Simons Array(CMB) + DESI(BAO) + SKA 2(21cm line). 25 /44

◆ Dark energy equation of state (EoS)
K. Kohri, Y. Oyama, T. Sekiguchi,
T. Takahashi, arXiv:1608.01601.

26 /44

Dark energyFriedmann ⽅程式7𝑎̇8𝜋7𝐻 ==
𝜌𝑎3

𝑎̈4𝜋
4𝜋
=−
𝜌 + 3𝑝 = −𝜌 1 + 3𝑤
𝑎33Equation of state (EoS) : 𝑤 =ESA, Planck, http://sci.esa.int/planck/8ãä̈𝑤 < − の時，0 < となり加速膨張が実現するGä(dark energy)
𝑤 = −1 の時は𝜌 = constant となりcosmological constant
27 /44

Dynamical dark energy
Expansion ratio of the Universe (Hubble parameter)
𝐻7 = 𝐻p7

ΩQ 𝑎2G + Ωé 𝑎2³ + Ω¥ 𝑎27 + Ωê exp

8𝑑𝑎ì3 ë ì 1 + 𝑤ê (𝑎ì )ä 𝑎Contribution of the dark energy
⼀般には dark energyのEoSは Equation of state (EOS)𝑝ê (𝑎)
時間依存するように，𝑤ê (𝑎) ≡𝜌ê (𝑎)拡張した場合も考えられる．
本研究では，そのような時間依存するdark energy(𝑤ê ≠ constant)に対する，21cm線観測の将来的な感度について調べた．
28 /44

◆ Energy density of the dark energy8𝑑𝑎ì𝜌ê = 𝜌êp exp 3 ë1 + 𝑤 𝑎ìä 𝑎′

CPL parametrization𝜌ê (𝑧) = 𝜌êp 1 + 𝑧 G 8îïð îï| exp −

3𝑤8 𝑧
1+𝑧

HM parametrization (Suddenly changing model)𝜌ê (𝑧) = 𝜌êp 1 + 𝑧 G 8îïð𝑤p + 𝑤8 1 + 𝑧}
𝑤p 1 + 𝑧 + 𝑤8 1 + 𝑧}

G ïð 2ï| /Wetterich parametrization (Early dark energy model)𝜌ê (𝑧) = 𝜌êp 1 + 𝑧

G 8î€ñ ò,𝛼ê 𝑧 =𝑤p1 + 𝑏 log 1 + 𝑧
29 /44

今回はこれについてだけ（制限に21cm線が⾮常に有効な場合がある）

◆ Parametrization of EoS [Hannestad, Mortsell 2004]
1+𝑧𝑎 + 𝑎}
1 + 𝑧}𝑤ê 𝑧 = 𝑤p 𝑤8= 𝑤p 𝑤81+𝑧
𝑤8 𝑎 + 𝑤p 𝑎}
𝑤8 + 𝑤p
1 + 𝑧}
1+𝑤ê suddenly changes at a transition redshift 𝑧} =𝑤88− 1.
äö𝑧} = 1, 𝑝 = 10𝑧} = 1, 𝑝 = 5𝑧} = 5, 𝑝 = 5𝑤p𝑝 represents a width of thetransition.

30 /44

◆ Energy density of the dark energyΩê 𝑧 ≡

𝜌ê 𝑧
8𝜋𝐺= 7𝜌 𝑧𝜌‰é-÷ 𝑧3𝑐 𝐻 𝑧 7 êHigh zの観測によって、近傍のSN等の観測より過去に31 /44transitionするような場合を原理的には制限可能

Alcock-Paczynski test (銀河サーベイ, 21cm line)
視線垂直⽅向𝑥 8 , 𝑥 7 = 𝑑Ú 𝑧∗ 𝜃8 , 𝑑Ú 𝑧∗ 𝜃 7⾓形距離𝑑Ú 𝑧∗ で決まる
𝑥8

視線垂直⽅向òì𝑑𝑧(𝑧 − 𝑧∗ )G𝑥 =ë~ì)𝐻(𝑧𝐻(𝑧∗ )ò∗

共動距離で決まる
揺らぎの2点相関で⾒た場合，BAOのスケールが間違った宇宙論パラメータの元では⾮等⽅に歪む

32 /44

◆ Expected constraint of HM parametrization
95% C.L. Contour

Transition :𝑎} = 0.1 (𝑧} = 9)
𝑝 = 100(transitionの幅)+Omniscope
Planck + DESI +JDEM (SNe Ia)+𝐻p+SKA pahse 2+SKA phase 1

BAO, SNe Ia のサーベイ範囲外でTransitionが⽣じるため，それらによる𝑤8 の制限は弱い

⼀⽅，よりhigh zの観測である21cm線は，𝑤8 に感度がある．
33 /44

◆ Constraining the light gravitino mass
Y. Oyama, M. Kawasaki,arXiv:1605.09191.

34 /44

◆Motivations
Light gravitino : 𝑚G/7 ≲ 𝒪 1 − 10 eV
The scenarios can be consistent with manyof baryogenesis/leptogenesis scenarios.

Since light gravitinos behave as warm dark
matter in late epochs, we can obtain theirsignature from matter fluctuations.
CMB lensing : K.Ichikawa et.al., 2009.
Cosmic Shear: A.Kamada et.al., 2014.

35 /44Effects of light gravitino on
the growth of density fluctuations
1. Increasing radiation
Light gravitinos contributethe energy density of radiation
at the early Universe.

2. Free streaming effect（Main signature）
Fluctuations of matter are
suppressed in small scales

36 /44

Temperature of light gravitino: 𝑻𝟑/𝟐
At the early Universe,
Light gravitinos are relativistic particles.

Effective number of neutrino species
𝜌G/7
𝑇G/7 ³𝑔∗z
𝑁G/7 ===
𝜌z
𝑇z𝑔∗G/7³/G

𝜌z: Energy density of one generation of neutrino

𝑇z: Temperature of neutrino𝑔∗z ：The effective degree of freedom
at decoupling of neutrinos (= 10.75)𝑔∗G/7 ：The effective degree of freedom
at decoupling of light gravitinos

37 /44

Free streaming effect of light gravitino
Matter power spectrum 𝑃 𝑘 = 𝛿¥ 7 (Linear, z=0)
Suppression
due to the freestreaming effectof light gravitino
𝒁=𝟎

𝑁G/7 = 0.059
Ω& ℎ7 is fixed

The free streaming
scale is about
0.1ℎMpc 28 ≲ 𝑘.

38 /44

Cosmological parameter set
Fiducial parameters
ΩQ ℎ7 , ΩO ℎ7 , Ω' , 𝑛} , 𝐴} , 𝜏, 𝑌
= (0.1417, 0.0223 0.6911 0.9667 2.142×102* , 0.066, 0.25)

Parameters related to light gravitino
𝜌G/7𝑁G/7 == 0.059 (𝑔∗G/7 = 90)𝜌zΩG/7𝑓G/7 ≡= 0.01071 （𝑚G/7 = 1 eV）
Ω$%
39 /44

Constraints on 𝒇𝟑/𝟐 (𝒇𝟑/𝟐 = 𝟎. 𝟎𝟏𝟎𝟕𝟏)
1𝜎 error of 𝒇𝟑/𝟐 ( 𝑁G/7 = 0.059 is fixed.)
Planck + Simons Array + DESI (BAO) + 𝑯𝟎
𝝈 𝒇𝟑/𝟐 = 𝟎. 𝟎𝟎𝟑𝟒𝟔 → 𝝈 𝒎𝟑/𝟐 = 𝟎. 𝟑𝟑 eV+ SKA 1

𝝈 𝒇𝟑/𝟐 = 𝟎. 𝟎𝟎𝟐𝟔𝟑 → 𝝈 𝒎𝟑/𝟐 = 𝟎. 𝟐𝟓 eV+ SKA 2

𝝈 𝒇𝟑/𝟐 = 𝟎. 𝟎𝟎𝟏𝟔𝟓 → 𝝈 𝒎𝟑/𝟐 = 𝟎. 𝟏𝟔 eV+ Omniscope
𝝈 𝒇𝟑/𝟐 = 𝟎. 𝟎𝟎𝟎𝟕𝟏 → 𝝈 𝒎𝟑/𝟐 = 𝟎. 𝟎𝟔𝟕 eV
40 /44

Constraints on 𝒇𝟑/𝟐 and 𝑵𝟑/𝟐
95% C.L. Contours
Planck+Simons Array +DESI + H0 + SKA2

𝒇𝟑/𝟐

Planck +Simons Array(SA)+DESI+H0+SKA 1+SKA 2+Omniscope

The combination
can detect
nonzero 𝑁G/7 .
(DESI is a future
observation of BAO.)
41 /44

Constraints on 𝒇𝟑/𝟐 and 𝚺𝐦𝝂
95% C.L. Contours in 𝑓G/7 − Σmz plane

Planck +Simons Array(SA)+DESI+H0+SKA 1+SKA 2+Omniscope

Planck+Simons Array +DESI + H0 + SKA1
They can discriminate
the signature oflight gravitinos
from that of neutrinos .

44 /44

◆ Contents
1. 21cm線観測の概要
2. SKA等の将来の21cm線観測による宇宙論モデルの制限(1) ニュートリノ質量(2) Dark energy(3) 軽いグラビティーノdark matter

3. Summary

43 /44

Summary■ We studied sensitivities of
21cm line + CMB observations
to several cosmological parameters■ Planck + Simons Array + SKA phase1
can detect the neutrino total mass at 2σ(if 𝚺𝒎𝝂 ~𝟎. 𝟏eV.)■ For the suddenly transition dark energy model,
21 cm observations can significantly improve theconstraints on the EoS parameters.
■ We found that SKA 1 and 2 can strongly improve
constraints of the mass of light gravitino 𝒎𝟑/𝟐 .
44 /44