Differentiating CDM and baryon
isocurvature perturbations from 21 cm line
observations
関口 豊和(名古屋大学)

Ref: M.Kawasaki TS, T.Takahashi
arXiv:1104.5591, published in JCAP2011年11月6日
理論懇シンポジウム@天文台
2011年12月10日土曜日

Isocurvature perturbations•Initial perturbation for structure formationisocurvature perturbations

nrad (�x)

2011年12月10日土曜日

nmatter (�x)curvature (adiabatic)
perturbations
nmatter (�x)nrad (�x)Isocurvature perturbations•Initial perturbation for structure formationisocurvature perturbations

nrad (�x)

2011年12月10日土曜日

nmatter (�x)curvature (adiabatic)
perturbations
nmatter (�x)nrad (�x)Isocurvature perturbations•Initial perturbation for structure formationisocurvature perturbations

nrad (�x)curvature (adiabatic)
perturbations
nmatter (�x)

nmatter (�x)3
CDM isocurvature (CI) SCI = δcdm − δγ
43baryon isocurvature (BI): SBI = δb − δγ4••2011年12月10日土曜日

nrad (�x)Isocurvature perturbations•Initial perturbation for structure formationisocurvature perturbations

nrad (�x)curvature (adiabatic)
perturbations
nmatter (�x)

nmatter (�x)3
CDM isocurvature (CI) SCI = δcdm − δγ
43baryon isocurvature (BI): SBI = δb − δγ4•••Models for isocurvature perturbations•axion model » CI
•Affleck-Dine mechanism » BI
•curvaton scenario » CI, BI

probe for generation mechanisms of CDM/baryon
2011年12月10日土曜日

nrad (�x)•δCan we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtoniana : scale factor
H = ȧ/aτ̇ = ane σT

2011年12月10日土曜日

•δ

Can we distinguish CI/BI?
cdm and δbin linear perturbation eqs.

•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]2011年12月10日土曜日

gauge:
conformal Newtoniana : scale factor
H = ȧ/aτ̇ = ane σT•δCan we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb and2011年12月10日土曜日

a : scale factor
H = ȧ/aτ̇ = ane σT•δCan we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb and•photon & baryon Euler eqs. (anisotropic stress neglected)kv̇γ = δγ + kΨ − τ̇ [vγ − vb ]44ρ̄γv̇b = −Hvb + kΨ +τ̇ [vγ − vb ]3ρ̄b

2011年12月10日土曜日

a : scale factor
H = ȧ/aτ̇ = ane σT•δCan we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb and•photon & baryon Euler eqs. (anisotropic stress neglected)kv̇γ = δγ + kΨ − τ̇ [vγ − vb ]44ρ̄γv̇b = −Hvb + kΨ +τ̇ [vγ − vb ]3ρ̄b

➡ No pressure gradient

2011年12月10日土曜日

a : scale factor
H = ȧ/aτ̇ = ane σT•δCan we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb and•photon & baryon Euler eqs. (anisotropic stress neglected)kv̇γ = δγ + kΨ − τ̇ [vγ − vb ]44ρ̄γv̇b = −Hvb + kΨ +τ̇ [vγ − vb ]3ρ̄b

➡ No pressure gradient

2011年12月10日土曜日

a : scale factor
H = ȧ/aτ̇ = ane σTmomentum transfer only•δ

Can we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb anda : scale factor
H = ȧ/aτ̇ = ane σT•photon & baryon Euler eqs. (anisotropic stress neglected)kv̇γ = δγ + kΨ − τ̇ [vγ − vb ]44ρ̄γv̇b = −Hvb + kΨ +τ̇ [vγ − vb ]3ρ̄bmomentum transfer only

➡ No pressure gradientand2011年12月10日土曜日

affect the CMB and metric perturbations only in combination of.

•δ

Can we distinguish CI/BI?
cdm and δbin linear perturbation eqs.
gauge:
conformal Newtonian•Poisson eq.
k 2 Φ = 4πGa2 ρ̄tot [δtot + (1 + wtot )vtot ]No difference btw. δb anda : scale factor
H = ȧ/aτ̇ = ane σT•photon & baryon Euler eqs. (anisotropic stress neglected)kv̇γ = δγ + kΨ − τ̇ [vγ − vb ]44ρ̄γv̇b = −Hvb + kΨ +τ̇ [vγ − vb ]3ρ̄bmomentum transfer only

➡ No pressure gradientandaffect the CMB and metric perturbations only in combination of

CI/BI cannot be discriminated by observations of CMB,
total matter and metric perturbations.

.

Ωcdm
Ωb
SCI +
SBI .
These are only sensitive to total matter isocurvature Sm =ΩmΩm

2011年12月10日土曜日

How can we distinguish CI/BI?
need observations which is sensitive to δ (or δ•inWetheform other than δ .
bm

21 cm line observation is promising since it can•measureδ directly.
b

We investigate to what extent CI/BI can be•discriminatedfrom future 21 cm surveys.

2011年12月10日土曜日

cdm )•21cm line

Redshifted 21 cm line (1)transition btw. hyperfine splitting states of a hydrogen atom

tripletν0 � 1.4 GHzhν0= 68 mKT∗ =kB

singletspontaneous emission rate
A10 = 2.85 × 10−15 s−1•brightness temperature
Tb = (1 − e−τ21cm )Ts + e−τ21cm TCMB•

Spin temperature

HI gasat redshift z:
observed at•21 cm optical depth

3λ20 hcA10 nHI (z)τ21cm (z) =32πkB Ts (z)H(z)2011年12月10日土曜日

emission/absorption
optical depth:

photonRedshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

9

10

10

8

1/2
4000C104 /mK

10

0

100τ!

7

10

−1
(κpH
10 np )

ï10

6

T /K or years

10

5

10

ï20

−1
(κeH
10 ne )
4

10

T" /(A10 Tγ )

ï30

3

10

Tγ

∆Tb /mK

2

10

Ts

1

10

ï40

Tg

−1
(κHH
10 nH )

0

10

10

100

z
2011年12月10日土曜日

1000

ï50
20

30

50

100

200

z

500

Lewis & Challinor 2007

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

9

10

10

8

1/2
4000C104 /mK

10

0

100τ!

7

10

−1
(κpH
10 np )

ï10

6

T /K or years

10

less
signal5

10foregrounds
dominate

ï20

−1
(κeH
10 ne )
4

10

T" /(A10 Tγ )

ï30

3

10

Tγ

∆Tb /mK

2

10

Ts

1

10

ï40

Tg

−1
(κHH
10 nH )

0

10

10

100

z
2011年12月10日土曜日

1000

ï50
20

30

50

100

200

z

500

Lewis & Challinor 2007

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

2011年12月10日土曜日

τ21cm

Ts < TCMB .

∆Tb < 0 : absorption

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB

2011年12月10日土曜日: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
δ(Ts −TCMB )2011年12月10日土曜日

δτ21cm: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

2011年12月10日土曜日

depends only on δm: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

21 cm can probe
2011年12月10日土曜日

depends only on δm, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δmisotropic

21 cm can probe
2011年12月10日土曜日, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δmisotropic

21 cm can probe
2011年12月10日土曜日, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightnessT temperature−T∆Tb = Tb − TCMB �

s

CMB

1+z

At high redshift z>30
(prior to formation of first objects),

τ21cm∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δm: line-of-sightdirectionisotropic

Tomography helps the separation!
21 cm can probe
2011年12月10日土曜日, separately from.

21 cm power spectrum•2d anisotropic power spectrum•

[

[

[

[

[


FFTT sensitivity

niso = 3

N>>0SF@

pure CI

3 N__N> >P.0+]@

3 N__N> >P.0+]@

−1
P
(k
)/P
(k
)
=
0.1
at
k
=
0.0002Mpc
å Sm 0
AD 0
0



z = 50, k� = 0.06Mpc−1

[

[

[
pure BIniso = 2



N>>0SF@using “CAMB source”
Lewis & Challinor 2007

CI & BI can be in principle distinguished by 21 cm observations.
2011年12月10日土曜日

Future constraint• Fisher matrix analysis with (ωb , ωc , H0 , τreion , nadi , Aadi , rCI , rBI , niso )rCI = PCI (k0 )/Padi (k0 ), rBI = PBI (k0 )/Padi (k0 ) at k0 = 0.0002Mpc−1

niso = 3

CMBpol alone

niso = 2rBI

2d constraints

CMBpol+FFTT@ z=30, 40, 50

rCI

rCI

Future 21 cm surveys can distinguish CI/BI if
2011年12月10日土曜日.

*fiducial model:
pure CI(rCI , rBI ) = (0.1, 0)

Blue-tilted isocurvature
perturbations?
from recent observations?
•Preference
PHYSICAL REVIEW D 83, 123517 (2011)

Bean+ 06, Keskitalo+ 06, Sollom+ 09, Li+ 10, etc.

Li+ 10

Data={WMAP7, ACBAR, CBI, Boomerang,
SDSS LRG, Union SNeIa}

niso

3
2

niso � 2 ∼ 3

1
HONG LI et al.

3.3

PHYSICAL REVIEW D 83, 123517 (2011)−2
0
TABLE II. The mean values and 1!10errors of the parameters related to the mixed initial adiabatic and CDM isocurvatureln[10Aiso
Aiso ]
perturbations.
0.32

•

Ωm

Adiabatic
Mixed

−4

log½1010 Aadis "3:204 $ 0:036
0.3 3:165 $ 0:044

nadis
0:964 $ 0:010
0:972 $ 0:014

0.28

From the mixed initial conditions, the constraints on theSometheoreticalmodels
10 Aadi " ¼ 3:165 $ 0:044
adiabatic perturbation
are log½10
0.26
s$ 0:014 at&68%
confidence09,
level.etc.
Theand nadis ¼ 0:972
KasuyaKawasaki
adiabatic spectrum
0.24 index becomes larger, when comparing
2011年12月10日土曜日
with the constraint nadi
s ¼ 0:964 $ 0:010ð1!Þ from thelog½1010 Aiso
s "

niso
s

cos!

"2min

–
'1:375þ1:233'1:306–
2:246þ0:494'0:428–0:094þ0:075'0:0958217.08213.5slightly smaller !m and larger #, and this is due to thecorrelation of the CDM isocurvature perturbations withother cosmological parameters when considering the nonadiabatic initial condition in our analysis.
The correlations among the isocurvature mode parame-

Blue-tilted isocurvature
perturbations?
from recent observations?
•Preference
PHYSICAL REVIEW D 83, 123517 (2011)

Bean+ 06, Keskitalo+ 06, Sollom+ 09, Li+ 10, etc.

Li+ 10

Data={WMAP7, ACBAR, CBI, Boomerang,
SDSS LRG, Union SNeIa}

niso

3
2

niso � 2 ∼ 3

1
HONG LI et al.

3.3

PHYSICAL REVIEW D 83, 123517 (2011)−2
0
TABLE II. The mean values and 1!10errors of the parameters related to the mixed initial adiabatic and CDM isocurvatureln[10Aiso
Aiso ]
perturbations.
0.32

•

Ωm

Adiabatic
Mixed

−4

log½1010 Aadis "3:204 $ 0:036
0.3 3:165 $ 0:044

nadis
0:964 $ 0:010
0:972 $ 0:014

0.28

From the mixed initial conditions, the constraints on theSometheoreticalmodels
10 Aadi " ¼ 3:165 $ 0:044
adiabatic perturbation
are log½10
0.26
s$ 0:014 at&68%
confidence09,
level.etc.
Theand nadis ¼ 0:972
KasuyaKawasaki
adiabatic spectrum
0.24 index becomes larger, when comparing
2011年12月10日土曜日
with the constraint nadi
s ¼ 0:964 $ 0:010ð1!Þ from thelog½1010 Aiso
s "

niso
s

cos!

"2min

–
'1:375þ1:233'1:306–
2:246þ0:494'0:428–0:094þ0:075'0:0958217.08213.5slightly smaller !m and larger #, and this is due to thecorrelation of thewith
To beisocurvaturecheckedperturbations
by Planck➡CDMother cosmological parameters when considering the nonadiabatic initial condition in our analysis.
The correlations among the isocurvature mode parame-Summary
We investigated possibility for distinguishing CDM and baryon•isocurvaturemodes.
21 cm observations can probe the fluctuation of baryon•separatelyfrom total matter perturbations, and in principle
distinguish CI/BI, which is difficult from other cosmologicalobservations, such as CMB.

Future 21 cm tomography surveys (FFTT etc.) can distinguish•thesetwo isocurvature modes, if their power spectra are very
blue-tilted.

2011年12月10日土曜日

Thank you for your attention!

2011年12月10日土曜日

•photon

Full set of perturbation eqs.
(in synchronous gauge)•baryon142 ˙
δ̇γ = − vγ − hL
3
3
�
�
1
2
v̇γ = kδγ − σγ − aσT ne (vγ − vb )4

•massless neutrino

42 ˙
δ̇ν = − vν − hL
3
3
�
�
1
2
v̇ν = kδν − σν .
4δ̇b = −vb − h˙L24ρ̄γv̇b = Hvb −aσT ne (vγ − vb )
3ρ̄b

•CDM

pressure gradient1 ˙δ̇c = −vc − hL
2Thomson scatterv̇c = Hvc

•Einstein eq.

1k ηT − HḣL = −4πGa2 ρ̄tot δtot22

k 2 η̇T = −4πGa2 (ρ̄tot + p̄tot )vtot
2011年12月10日土曜日

andonly appear in the form of.

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),

Ts < TCMB .

∆Tb < 0 : absorption: line-of-sightdirection

2011年12月10日土曜日

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB

2011年12月10日土曜日: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
δ(Ts −TCMB )2011年12月10日土曜日

δτ21cm: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),

Ts < TCMB .

∆Tb < 0 : absorption•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

2011年12月10日土曜日

depends only on δm: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

21 cm can probe
2011年12月10日土曜日

depends only on δm, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δmisotropic

21 cm can probe
2011年12月10日土曜日, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δmisotropic

21 cm can probe
2011年12月10日土曜日, separately from.

: line-of-sightdirection

Redshifted 21 cm line (2)•Differential brightness temperature

Ts − TCMB∆Tb = Tb − TCMB �
τ21cm
1+z

At high redshift z>30
(prior to formation of first objects),∆Tb < 0 : absorption

Ts < TCMB .

•Fluctuations in 21 cm brightness temperatureT̄CMBn̂ · d�vb /dr
δ21cm ≈
(δTs − δTCMB ) + δnHI −H
T̄s − T̄CMB
depends on

depends only on δm: line-of-sightdirectionisotropic

Tomography helps the separation!
21 cm can probe
2011年12月10日土曜日, separately from.

Evolution of spin temperature
910

Ts is affected by

810• Absorption of CMB photons

7

10

−1
(κpH
10 np )

• Atomic (H-H, H-p, H-e) collision
6• Scattering of UV photons(after formation of first objects)

T /K or years

10

5

10

−1
(κeH
10 ne )
4

10

T" /(A10 Tγ )

3

10

Tγ
2

10

Ts

1

10

Tg

−1
(κHH
10 nH )

0

10

10

100

z

Lewis & Challinor 20072011年12月10日土曜日

1000

Evolution of brightness temperature•optical depth of 21 cm line emission/absorption

3λ0 hcA10 n̄HI(z)
τ21cm (z) =32πkB T̄s H
�
�
�1/2
�−1 �
�
�
�
−1/2
Ts
ωm
1+z
ωb
−2
� 1.08 × 10 xHI(z)
TCMB
0.023 0.13
1010•Differential brightness temperature
Ts − TCMB
∆Tb =
τ21cm
1+z

1/2
4000C104 /mK

0

ï10

less
signal100τ!

foregrounds
dominate

ï20

ï30∆Tb /mK
ï40

Lewis & Challinor 20072011年12月10日土曜日

ï50
20

30

50

100

200

z

500

21 cm tomography
Consider an observation at around frequency ν ;•frequency differencer� = y(zν )∆νν0−1
central redshift: zν =νdistance in line-of-sight direction(1 + z)2
y(z) =
ν0 H(z)•sky-position

distance in transverse direction
� zdz �dA (z) =��r⊥ = dA (zν )Θ
�
0 H(z )

•correspondence in Fourier space �k� = u� /y(zν )�k⊥ = �u⊥ /dA (zν )f (�u) =f (�k) =�Observed data resides in u-space
2011年12月10日土曜日

�� exp i(∆νu� + Θ
� · �u⊥ )d∆νd2 Θ f (∆ν, Θ)��
d3 r f (�r) exp i�r · �k�Fisher matrix of 21 cm tomography•Fisher matrix �[Tegmark 1997](21cm)
Fij
=

d3 u
VΘ
(2π)3 [P (tot) (�u)]2∆Tb�(signal)∂P∆Tb (�u)

∂λi

��

(signal)∂P∆Tb (�u)

∂λj

�

.

λi cosmological parameter: survey volume•limitation in k-space volume
k < knl � 0.1Mpc−1 : linear evolutionk� > 1/y(z)B : foreground removal•signal+noise covariance(tot)(signal)P∆Tb (�u) = P∆Tb
2011年12月10日土曜日(noise)(�u) + P∆Tb(�u)

B : band width

FFTT parameters•FFTT noise power spectrum[Tegmark & Zaldarriaga 2009]

2 2
4πf
λ
sky
ν Tsysnoise
P∆Tb (�u) =W (�u⊥ )2AΩFoV fcover tobs

• survey volume

sky coveragearray areaantenna coverage
Field of View
system temperature(Galactic synchrotron)
observation timeBand width
2011年12月10日土曜日• Gaussian window function

k -dependence
||

10-4

error
pure CI
pure BIP(k||,k))[mK2 MHz]P(k||,k))[mK2 MHz]

10-4

10-5

error
pure CI
pure BI

10-5niso=3, z=50, k||=0.06 Mpc-1
10-6 -4
10

10

-3

10

-2

niso=3, z=50, k||=0.02 Mpc-1
10-1

k[Mpc-1]

P(k||,k))[mK2 MHz]error
pure CI
pure BI

10-5niso=3, z=50, k||=0.006 Mpc-1
10-3

10-2
k[Mpc-1]

2011年12月10日土曜日

10-3

10-2
k[Mpc-1]

10-4

10-6 -4
10

10-6 -4
10

10-1

10-1

redshift-dependence
10-5

10-4

error
pure CI
pure BI2

P(k||,k))[mK MHz]P(k||,k))[mK2 MHz]error
pure CI
pure BI

10-5niso=3, z=30, k||=0.06 Mpc-1
10-6 -4
10

10

-3

10

-2

niso=3, z=40, k||=0.06 Mpc-1
10-1

k[Mpc-1]

P(k||,k))[mK2 MHz]error
pure CI
pure BI

10-5niso=3, z=50, k||=0.06 Mpc-1
10-3

10-2
-1

k[Mpc ]2011年12月10日土曜日

10-3

10-2
k[Mpc-1]

10-4

10-6 -4
10

10-6 -4
10

10-1

10-1

n_iso-dependence
10-4

error
pure CI
pure BIP(k||,k))[mK2 MHz]P(k||,k))[mK2 MHz]

10-4

10-5

error
pure CI
pure BI

10-5niso=1, z=30, k||=0.06 Mpc-1
10-6 -4
10

10

-3

10

-2

niso=2, z=50, k||=0.06 Mpc-1
10-1

k[Mpc-1]

P(k||,k))[mK2 MHz]error
pure CI
pure BI

10-5niso=3, z=50, k||=0.06 Mpc-1
10-3

10-2
k[Mpc-1]

2011年12月10日土曜日

10-3

10-2
k[Mpc-1]

10-4

10-6 -4
10

10-6 -4
10

10-1

10-1

constraint for n_iso=2

2011年12月10日土曜日

constraint for n_iso=3

2011年12月10日土曜日

distinction from CMB?

2011年12月10日土曜日