CMB?????/ CMB??????

1
??????????? 1
2006/08/13-14 ????????? ???????????????????
????

• ?? ??
• (???)

2
??
????
??????????
CMB?????/ CMB??????
?????
CMB????4????
????????????????
???
3
??
S.Dodelson, Modern Cosmology (Academic Press,
2003)
?????, ?????? (?????, 2000)
W.Hu, Wandering in the Background (Thesis,
1995)
Hu Sugiyama, Phys.Rev.D 51, 2599 (1995)
ApJ 444, 489 (1995)
ApJ 471, 542 (1996)
4
CMB?????(1)
Cosmic Microwave Background
???????????
????????????????????????
0????
(????)
????2.7K???????
1????
(??????)
0.01 ??????????
Sachs-Wolfe ?????????
????????
CMB?????????????????????
5
CMB?????(2)
CMB ???????????????????????
??????????????
???????????????2???????
(??????SZ??,??????etc.)
CMB anisotropy ???????

• ???????????? (????????)

• ??????????????

• ???????????(?????)

????(????????)?????
????
6
CMB?????? (1)
????????????? ?????(????)???????
??????
?????????
??
?????
??
??
????
?????? 38?? 10?? 100?? ??
7
CMB?????? (2)
(???????????)????????????????????????????
??????
??????? (? ?????????)
??????(ct)
Physical length
?????
??
????????
????
????
8
CMB?????? (3)
0????
???????
?????????
????????????
??????
1????
???????
?????????????
????????????
??????
CMB ???
??(??)
??????
??????
??
????? ???
CDM
????(??)
9
?????(1)
?????????
a1 ???
??????????????
????????
????????
10
Distance-Redshift Relation
Comoving radial distance
Angular diameter distance
Luminosity distance
11
Distance-Redshift Relation
12
?????(2)
(??)??????????
Saha??
(????)
Peebles??
(?????)
?
??n2???????????????
13
Recombination History
RECFAST
Saha??
Multi-level calculation ???????????????????
RECFAST
Seager, Sasselov Scott, (1999)
CMBFAST ??????????????
14
?????(4)
?????????
????????????(??????)
??????????????(?????)????
??????
Newton ??????
?????
????????????
??????
???????????
?????
15
?????(5)
????????????
Cf
???
???????????
??(??)
??????
??????????
???? (??)
??????
??????????
??
CDM
?????? (massless)
???????????
??
16
?????(5)
??????
?????
??(??)
????????
???? (??)
CDM
????
?????? (massless)
17
????
??(???????)?????????????????? µ ?????
??????????
??????????
?????????????????
????(????????)
??????????
18
?????(6)
???????????
Longitudinal gauge
(00)-????
(ij)-?????????????
??????
???????
19
?????????
(0th-1)
(0th-2)
(1st-1)
(1st-2)
(1st-3)
(1st-4)
(1st-5)
(1st-8)
(1st-6)
(1st-9)
(1st-7)
20
How to Solve Equations
?????????????????
???????
CMBFAST, CAMB, CMBEASY,
0.1????????CMB???????????? ??????????????????????
??
????
????
???????
21
????
??????????????????????????????
????????????
(?????)
(???????????????????)

• ????????

• ???????????

22
???????CMB

• ?????????

?????
????????
?? ????????
???

• ???????????

?????????????
?????? ?????1 ????
(?)
23
?????
adiabatic
???????
?????????
isocurvature
ns1 (adiabatic)
ns2 (isocurvature)
by CMBFAST4.5.1
24
Primary Anisotropy

• Sachs-Wolfe(SW) effect

(??????????)???????????

• Integrated Sachs-Wolfe (ISW) effect

???????????????????????

• Acoustic oscillation

???????????????

• Diffusion damping

CDM??????????
25
Primary Anisotropy Cl
Log scale
Linear scale
Acoustic oscillation
Acoustic oscillation
ISW effect
SW effect
SW effect
Diffusion damping
26
Integral solution
??
?????
(1st-1)
???
?????????????
27
Visibility function Optical depth
Visibility function
Optical depth
h
Last scattering surface (?????)
28
Approximate Expression
Visibility function ????????
(?)
????? ???
Early type
Integrated Sachs-Wolfe ?
Late type
(Recombination?????)
29
Large-scale Anisotropy
(?) ???1,2??????????????? (1st-1)
????? (k?0)
??????
?
?????
??????
?????????Sachs-Wolfe ???
??????????
30
Simple Derivation of Factor 1/3
(W.Hu, Lecture note ??)
31
Small-scale Anisotropy
????? (?) ???1?2????????
????? ????????
???????????
(1st-1)
(1st-4)
?????????? ??????
(1st-1)
?
?????????
(1st-4)
32
Tight-coupling Approximation
(1st-1)
(1st-4)
(1st-4)
(1st-1) ?2????
(1st-1) ?1??????(d/dh)???????????
33
Acoustic Oscillation(1)
?????????????
sound velocity of baryon-photon fluid
WKB???
C1, C2 ?????
sound horizon
34
Acoustic Oscillation(2)
????? (?) ???1?
???
???
??
??
????????????????????????????????
35
????(1)

• ????????cos???????????sin?

(?????)
??????
(??????)

• ????????????????????

cos or sin
(?) ????
(? flat ???)
36
????(2)
(??)
?????
Comoving angular diameter distance

• Diffusion damping

Tight-coupling ???????
???????????????
37
????????????(1)
???????????
?????
38
????????????(2)
?????????????
?????
39
??????????
Baryon acoustic oscillation (BAO)
Percival et al. astro-ph/0608636
???????????????? P(k) ??????
SDSS Main sample LRG (77800?)
?????????????????????????????
?????????????????????-??????????
???????????
40
Velocity overshoot effect
????????
Growing mode
?????
Decaying mode
??
Tight-coupling limit
(????????)
41
Evolution of linear P(k)
42
Secondary Anisotropy

• ???????

Zaldarriaga (1997)

• ???????

Zaldarriaga Seljak (1998)
Seljak (1996)

• Sunyaev-Zeldovich (SZ) ??

Komatsu Kitayama (1999) Komatsu Seljak (2002)

• Ostriker-Vishniac (OV) ??

• Rees-Sciama (RS) ??

43
Variation of Angular Spectrum
????????
(Thomson optical depth)
????????
???????
???????
44
Cl of secondary anisotropy
(Hu Dodelson 2002)
??????????primary anisotropy ????????????????????
45
???

• CMB???????

??????????????
????????????
????????????
??????

• CMB????4????

Sachs Wolfe
??????????
???
Integrated Sachs Wolfe
???????????
Acoustic oscillation
?????????????????
Diffusion damping
??????CDM?????
???
46
??
47
Legendre polynomial
??
(???)
(????)
48
More on Cosmological Dependencies
Angular projection
Late-time ISW
Late-time ISW
Fiducial model parameters
Baryon compression
Early-time ISW
Hu Dodelson (2002)