Transcript 宇宙学 - 中国科学院理论物理研究所

宇宙微波背景辐射
郭宗宽
中国科学院研究生院
2013.06.18
交叉学科：宇宙学
•
宇宙学基本假设和理论基础
宇宙学原理（无边，无中心）
爱因斯坦引力理论
宇宙物质（重子+光子+中微子+暗物质+暗能量）
•
观测实验的重要性
3个观测：星系红移，原初核丰度，宇宙微波背景辐射
超新星，大尺度结构 (2dFGRS,SDSS,LSST)，宇宙微波背景辐射，
宇宙射线 (Fermi-LAT,PAMELA,AMS-02)，21厘米谱线，射电波 (SKA)，
弱引力透镜，引力波，中微子
•
目前的进展和存在的问题
宇宙加速膨胀（暴涨，暗能量，修改引力，非均匀宇宙）
宇宙大尺度结构形成（冷/温/热暗物质，暗物质粒子的性质，暗物质分布）
Adam G. Riess Saul Perlmutter Brian P. Schmidt
The Nobel Prize in Physics 2011 was divided, one half awarded
to Saul Perlmutter (leader of SCP), the other half jointly to Brian
P. Schmidt (leader of High-Z) and Adam G. Riess (High-Z) "for
the discovery of the accelerating expansion of the Universe
through observations of distant supernovae".
A.G. Riess et al., Astron. J. 116 (1998) 1009 [arXiv:astro-ph/9805201]
S. Perlmutter et al., Astrophys. J. 517 (1999) 565 [arXiv:astro-ph/9812133]
内容
1.
2.
3.
4.
5.
6.
宇宙微波背景（CMB）辐射的形成
CMB的发现和探测实验
CMB的数据分析
CMB各向异性的物理起源
CMB的宇宙学解释
现状与展望
1. CMB的形成

p  e  H 
the reaction rate vs.
the expansion rate
decoupling during
recombination
2. CMB的发现和探测实验
 The CMB was first predicted
by G. Gamow, R. Alpher and
R. Herman in 1948
T~5 K
 the first discovery of the CMB
radiation in 1964-1965 the Nobel
Prize in Physics 1978:
A.A. Penzias and R.W. Wilson
 It is interpreted by R. Wilson, B. Burke, R. Dicke and J. Peebles
in 1965.
 COBE (Cosmic Background Explorer) - the first generation CMB
experiment, launched on 18 Nov. 1989, 4 years
the Nobel Prize in Physics 2006: J.C. Mather and G.F. Smoot
Hot big bang
J.C. Mather
G.F. Smoot (DMR)
isotropy
 the COBE satellite experiments:
① the Far InfraRed Absolute
Spectrophotometer (FIRAS)
team
② the Differential Microwave
Radiometer (DMR) team
 advantages of satellite
experiments:
• no atmospheric thermal emission
• full-sky map
 WMAP (Wilkinson Microwave Anisotropy Probe) - the second
generation CMB experiment, launched on 30 June 2001, 9 years
141°
23 GHz
33 GHz
41 GHz
61 GHz
• free-free emission: electron-ion scattering
• synchrotron emission: the acceleration of cosmic ray
electrons in magnetic fields
• thermal emission from dust
94 GHz
• foreground mask
• angular power spectrum of CMB
• WMAP science team publications
a)
b)
c)
d)
e)
2003, WMAP1, 14 papers, cited by 6873 records
2007, WMAP3, 5 papers, cited by 5289 records
2009, WMAP5, 8 papers, cited by 3527 records
2011, WMAP7, 6 papers, cited by 3803 records
2012, WMAP9, 2 papers, cited by 303 records
We have entered a new era of precision cosmology.
 Planck - the third generation CMB experiment, launched
on 14 May 2009, 30 months, 5 full-sky surveys
LFI: 30,44,70 GHz
HFI : 100,143,217,353,545,857 GHz
•
•
•
•
high sensitivity
wide frequency
full-sky coverage
high resolution ~7º,15′,5′
cosmological parameters
the temperature
angular power
spectrum
20 March 2013,
29 papers
 next generation space-based CMB experiment
• NASA: CMBPol
• ESA: COrE
 Other experiments
• ground-based experiments
ACBAR, BICEP, CBI, VSA, QUaD, BICEP2, …
ACT, ACTPol from 2013
SPT, SPTpol from 2012
QUBIC (r~0.01,bolometer, interferometer)
• balloon-borne experiments
BOOMRANG, MAXIMA, …
EBEX
Spider
 South Pole Telescope (SPT)
10 meter telescope
3 frequencies (95, 150 and 220 GHz)
arXiv:1105.3182: SPT+WMAP7+BAO+H0
𝑁eff = 3.86 ± 0.42
arXiv:1212.6267: SPT+WMAP7+BAO+H0
∑𝑚𝜈 = 0.32 ± 0.11 eV
 Atacama Cosmology Telescope (ACT)
3 frequencies (148, 218, and 277 GHz)
6 meter telescope
3. CMB的数据分析
time-ordered data
full sky map
spectrum
parameter estimates
 time-ordered data
d t  Pti m i  n t
 the temperature anisotropies can be expanded in spherical harmonics
 T ( ,  )

T
a
lm

a Y
lm
lm
( ,  )
lm
 d
 T ( ,  )
T
Y
*
lm
( ,  )
 for Gaussian random fluctuations, the statistical properties of the
temperature field are determined by the angular power spectrum
a lm a l ' m '  C l  ll ' mm '
*
T
For a full sky, noiseless experiments,
C
 cosmological parameter estimation
likelihood function for a full sky:
the sky-cut, MCMC
T
l

1
l

2l  1 m   l
a lm
2
4. CMB各向异性的物理起源
• primary CMB anisotropies (at recombination)
① inflation model (Alan H. Guth in 1981)
② primordial power spectrum of perturbations
③ angular power spectrum of CMB anisotropies
• secondary CMB anisotropies (after recombination)
①
②
③
④
thermal/kinetic Sunyaev-Zel’dovich effect
integrated Sachs-Wolf effect
reionization
weak lensing effect
 inflation model
V (φ)
reheating
inflation
φ
for slow-roll inflation, the primordial
power spectra of scalar/tensor
perturbations:
 the coupled, linearized Boltzmann, Einstein and fluid equations
𝑓 𝑥, 𝑞, 𝑛, 𝜏 = 𝑓0 (𝑞) 1 + Ψ(𝑥, 𝑞, 𝑛, 𝜏)
𝑔𝑠
1
𝑓0 𝑞 = 3 𝜖(𝑞)/𝑘 𝑇∓1
𝐵
ℎ 𝑒
∆𝑇
𝑑 ln 𝑓0
∆(𝑥, 𝑛, 𝜏) ≡
=−
𝑇
𝑑 ln 𝑞
−1
Ψ
the metric in the synchronous gauge
𝑑𝑠 2 = 𝑎2 𝜏 [−𝑑𝜏 2 + (𝛿𝑖𝑗 + ℎ𝑖𝑗 )𝑑𝑥 𝑖 𝑑𝑥 𝑗 ]
ℎ𝑖𝑗 (𝑥, 𝜏) =
1
ℎ𝑖𝑗 = ℎ𝛿𝑖𝑗 + ℎ𝑖𝑗 ∥ + ℎ𝑖𝑗 ⊥ + ℎ𝑖𝑗 𝑇
3
1
3
𝑖𝑘∙𝑥
𝑑 𝑘𝑒 [𝑘𝑖 𝑘𝑗 ℎ 𝑘, 𝜏 + 𝑘𝑖 𝑘𝑗 − 𝛿𝑖𝑗 6𝜂(𝑘, 𝜏)]
3
the Einstein equations
ℋ2
8𝜋 2
=
𝐺𝑎
3
the equations of state
𝜌𝑖 ,
𝑖
4𝜋 2
ℋ = − 𝐺𝑎
3
𝜔𝑖 = 𝑃𝑖 /𝜌𝑖
(𝜌𝑖 +3𝑃𝑖 )
𝑖
the linearized Einstein equations in k-space
1
2
𝑘 𝜂 − ℋ ℎ = −4𝜋𝐺𝑎2
𝛿𝜌𝑖
2
𝑖
𝑘 2 𝜂 = 4𝜋𝐺𝑎2
(𝜌𝑖 + 𝑃𝑖 )𝜃𝑖
𝑖
ℎ + 2ℋ ℎ − 2𝑘 2 𝜂 = −24𝜋𝐺𝑎2
𝛿𝑃𝑖
𝑖
ℎ + 6𝜂 + 2ℋ(ℎ + 6𝜂) − 2𝑘 2 𝜂 = −24𝜋𝐺𝑎2
(𝜌𝑖 + 𝑃𝑖 )𝜎𝑖
𝑖
the perturbed part of energy-momentum conservation equations for
the non-relativistic fluid (baryon, CDM, DE) in k-space
ℎ
𝛿𝑃
𝛿𝑖 = − 1 + 𝜔𝑖 𝜃𝑖 +
− 3ℋ
− 𝜔𝑖 𝛿𝑖
2
𝛿𝜌
𝜔𝑖
𝛿𝑃/𝛿𝜌 2
𝜃𝑖 = −ℋ 1 − 3𝜔𝑖 𝜃𝑖 −
𝜃𝑖 +
𝑘 𝛿 − 𝑘 2 𝜎𝑖
1 + 𝜔𝑖
1 + 𝜔𝑖
the Boltzmann equation in the synchronous gauge for the photon
and neutrino components in k-space
𝜕Ψ
𝑞
𝑑 ln 𝑓0
ℎ + 6𝜂
1 𝜕𝑓
2
+𝑖 𝑘∙𝑛 Ψ+
𝜂−
(𝑘 ∙ 𝑛) =
𝜕𝜏
𝜖
𝑑 ln 𝑞
2
𝑓0 𝜕𝜏
for massless particles
𝐹 𝑘, 𝑛, 𝜏 ≡
𝐶
𝑞 2 𝑑𝑞𝑞𝑓0 (𝑞)Ψ
𝑞 2 𝑑𝑞𝑞𝑓0
F is expanded in a Legendre series
∞
F 𝑘, 𝑛, 𝜏 =
−𝑖
𝑙
2𝑙 + 1 𝐹𝑙 (𝑘, 𝜏)𝑃𝑙 (𝑘 ∙ 𝑛)
𝑙=0
using 𝑃0 𝜇 = 1, 𝑃1 𝜇 = 𝜇, 𝑃2 𝜇 = (3𝜇2 − 1)/2, the recursion
relation and the orthonormality of the Legendre polynomials we
obtain a hierarchy.
 initial conditions
for the CMB photon
∆𝑇
𝑑 ln 𝑓0
∆ 𝑥, 𝑛, 𝜏 ≡
=−
𝑇
𝑑 ln 𝑞
∆ 𝑥, 𝑛, 𝜏 =
−1
𝐹𝛾
Ψ=
4
𝑑3 𝑘𝑒 𝑖𝑘∙𝑥 ∆ 𝑘, 𝑛, 𝜏
∞
∆ 𝑘, 𝑛, 𝜏 =
−𝑖
𝑙
2𝑙 + 1 ∆𝑙 (𝑘, 𝜏)𝑃𝑙 (𝑘 ∙ 𝑛)
𝑙=0
initial conditions (radiation-dominated, outside the horizon,
adiabatic mode, isocurvature mode)
∆𝑙 𝑘, 𝜏 = 𝜓(𝑘)∆𝑙 𝑘, 𝜏
𝜓(𝑘1 )𝜓(𝑘2 ) = 𝒫 𝑘 𝛿(𝑘1 + 𝑘1 )
 CMB anisotropy
expanded in spherical harmonics
∆ 𝑥0 , 𝑛, 𝜏0 =
𝑑3 𝑘𝑒 𝑖𝑘∙𝑥0 ∆ 𝑘, 𝑛, 𝜏0
∆ 𝑘, 𝑛, 𝜏0 =
𝑎𝑙𝑚 (𝑘, 𝜏0 )𝑌𝑙𝑚 (𝑛)
𝑙,𝑚
𝑎𝑙𝑚 𝑘, 𝜏0 =
𝑑Ω ∆ 𝑘, 𝑛, 𝜏0 𝑌𝑙𝑚 𝑛 = 4𝜋∆𝑙 (𝑘, 𝜏0 )𝑌𝑙𝑚 𝑘
the angular two-point correlation function
1
Δ(𝑥0 , 𝑛1 , 𝜏0 )Δ(𝑥0 , 𝑛2 , 𝜏0 ) =
4𝜋
∞
(2𝑙 + 1)𝐶𝑙 𝑃𝑙 (𝑛1 ∙ 𝑛2 )
𝑙=0
the angular power spectrum is
𝐶𝑙 = 4𝜋
𝑑𝑘
𝒫 𝑘 |∆𝑙 (𝑘, 𝜏0 )|2
𝑘
 features of spectrum
•
large angular scales
integrated SZ effect (<10)
Sachs-Wolf effect (10~100)
•
intermediate scales
acoustic oscillations (100~1000)
•
small scales (>1000)
Silk damping: the dissipation of small-scale perturbations caused by photons'
random walking out of overdense regions.
For full accuracy, the Boltzmann equation
must be solved to follow the evolution of
the photon distribution function.
5. CMB的宇宙学解释
The stronger the contraction, the higher these peaks should be.
6. 现状与展望
Planck may be the last space-based experiment
to measure the temperature spectrum.
 no evidence for non-Gaussianity; strong
constraints on non-Gaussianity
tension between Planck and astrophysical
measurements
anomalies in the WMAP/Planck data (the
quadrupole-octopole alignment, hemispherical
asymmetry, the cold spot, …)
detection of the primordial tensor perturbations
Thank you for your attention.