CMB物理
郭宗宽
lunch seminar, ITP/CAS
2014.4.8
内容
一、宇宙学发展现状
二、CMB物理
三、最新的CMB观测结果
四、中国的CMB物理
一、宇宙学发展现状
• 大爆炸宇宙学(1920s-1970s)
– 宇宙在膨胀（1929）
– BBN的预言与观测一致（1998）
– CMB的黑体谱（1994）
• 标准模型(1980s-2000s)
– 暴胀+Λ+冷暗物质+重子+中微子
• 精确宇宙学(2000s-now)
– CMB, LSS(BAO, GC, WL), SNIa
– 宇宙学不再是个传说
二、CMB物理
1.
2.
3.
4.
CMB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
1. CMB的形成
400 cm−3 now
𝑝 + 𝑒− ↔ 𝐻 + 𝛾
𝛾 + 𝑒− ↔ 𝛾 + 𝑒−
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
•
•
•
•
full-sky coverage
high sensitivity
wide frequency
high resolution ~ 5′(15′, 7º)
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, POLARBEAR, …
ACT, ACTPol from 2013
SPT, SPTpol from 2012
BICEP2 (r ~ 0.2)
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
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)
inflation model (Alan H. Guth in 1981)
 primordial power spectrum of perturbations
 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:
reconstruction of power spectrum
 parameterization:
•
•
•
𝑘
𝑘
ln 𝒫 𝑘 = ln 𝐴𝑠 + 𝑛𝑠 − 1 ln + 𝛼𝑠 ln
𝑘0
𝑘0
2
+⋯
scale-invariant (As)
power-law (As, ns)
running spectral index (As, ns, as)
𝑑 ln 𝒫(𝑘)
𝑑 ln 𝑘
 method:
ln 𝒫(𝑘) =
 advantages:
𝑑 ln 𝒫(𝑘)
𝑑 ln 𝑘
ln
𝑘𝑚𝑖𝑛
𝑘
𝑘𝑚𝑖𝑛
+ ln 𝒫(𝑘𝑚𝑖𝑛 ) ,
ln 𝒫 𝑘𝑖 ,
cubic spline,
𝑘
ln
+ ln 𝒫(𝑘𝑚𝑎𝑥 ) ,
𝑘𝑚𝑎𝑥
𝑘 < 𝑘𝑚𝑖𝑛
𝑘 ∈ {𝑘𝑖 }
𝑘𝑖 < 𝑘 < 𝑘𝑖+1
𝑘 > 𝑘𝑚𝑎𝑥
𝑘𝑚𝑎𝑥
• It is easy to detect deviations from a scale-invariant or a power-law spectrum.
• Negative values of the spectrum can be avoided by using ln P(k) instead of P(k).
• It reduces to the scale-invariant or power-law spectrum as a special case when
N bin= 1, 2, respectively.
WMAP7+H0+BAO
WMAP7+H0+BAO
WMAP7+ACT+H0+BAO
WMAP7+ACT+H0+BAO
ZK Guo, D.J. Schwarz, YZ Zhang, JCAP 08 (2011) 031;
ZK Guo, YZ Zhang, JCAP 11 (2011) 032;
ZK Guo, YZ Zhang, PRD 85 (2012) 103519.
CMB constraints on the energy scale of inflation
Determining the energy scale of inflation is crucial to understand the nature of
inflation in the early Universe.
ZK Guo, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011) 083522.
gravity
pressure
The stronger the contraction, the higher these peaks should be. Acoustic oscillations are
frozen in at recombination.
𝑄 ± 𝑖𝑈(𝑛) =
(𝐸𝑙𝑚 ∓ 𝑖𝐵𝑙𝑚 )∓2 𝑌𝑙𝑚 (𝑛)
𝑙𝑚
scalar
tensor 𝑟 = 0.22
三、最新的CMB观测结果
• 去年发布了Planck 2013温度数据
– 平静之下，暗潮汹涌。
• 上月发布了BICEP2极化数据
– 至于你信不信，我反正信了。
• 今年将发布Planck 2014极化数据
– 灭火器？
1.
2.
3.
4.
5.
6.
六参数的ΛCDM模型
原初非高斯性
暴胀模型
数据之间的不自洽
CMB温度涨落的反常
BICEP2分析结果
1. 六参数的ΛCDM模型
“None of these models are favoured over the standard six-parameter ΛCDM cosmology.”
Lorentz invariance violation in the neutrino sector
the deformed dispersion relation
𝐸 2 = 𝑚2 + 𝑝2 + 𝜉𝑝2
 CMB anisotropies:
(1) the energy density
𝛿𝜌𝜈 = (1 + 𝜉)−3/2 𝛿𝜌𝜈 (0) , ⋯
(2) the Boltzmann equation in the synchronous gauge
q

 l  (1   )
k
 2l  1
( l  1)  l 1  l  l 1    2 l 151 h   2 l
 
 
f ( x , q ,  )  f 0 ( q ) 1   ( x , q ,  )  ,
 
m a  (1   ) q
2
2
2
f0 (q ) 
2
5
   0 l
1
6
gs
1  exp(
1   q / T0 )

d ln f 0

h
0,
d ln q
,
 Big Bang nucleosynthesis:
(1) the energy density
𝜌𝜈 = (1 + 𝜉)−3/2 𝜌𝜈 (0)
(2) the weak reaction rate
Γ = 1 − 38𝜉 −
3(𝐶𝑉
4(𝐶𝑉
2
2
2
− 𝐶𝐴 )
2
+ 3𝐶𝐴 )
𝜉 (1 + 𝜉)−3/2 Γ (0)
 cosmological constraints:
data
the LIV parameter 𝝃
WMAP7+BAO+H0
0.077  0.089
Planck+BAO+H0 (forecast)
0.005  0.037
BBN
0.034  0.022
ZK Guo, QG Huang, RG Cai, YZ Zhang, PRD 86 (2012) 065004;
ZK Guo, JW Hu, PRD 87 (2013) 123519.
2. 原初非高斯性
“Planck finds no evidence for non-Gaussian statistics of the CMB anisotropies.”
3. 暴胀模型
slow-roll inflation (three parameters): As, ns, r, nt=-r/8
The data favor a concave potential rather than a convex one.
Inflation coupled to a GB term
 motivations:
higher-order corrections, a flat potential, a large tensor perturbation
 model:
𝑆=
𝑑 4 𝑥 −𝑔 12𝑅 − 12𝜕𝜇 𝜙𝜕𝜇 𝜙 − 𝑉 𝜙 − 12𝜉(𝜙) 𝑅2 𝐺𝐵 ,
where 𝑅2 𝐺𝐵 = 𝑅𝜇𝜈𝜌𝜎 𝑅𝜇𝜈𝜌𝜎 − 4𝑅𝜇𝜈 𝑅𝜇𝜈 + 𝑅2 .
introducing Hubble and GB flow parameters:
𝜖1 = −
𝐻
𝑑 ln 𝜖𝑖
𝑑 ln 𝛿𝑖
,
𝜖
=
,
𝛿
=
4
𝜉𝐻,
𝛿
=
,
𝑖+1
1
𝑖+1
𝐻2
𝑑 ln 𝑎
𝑑 ln 𝑎
the predicted tensor-to-scalar ratio and spectral indices:
𝑟 ≃ 8 2𝜖1 − 𝛿1 ,
2𝜖1 𝜖2 − 𝛿1 𝛿2
𝑛ℛ − 1 ≃ −2𝜖1 −
,
2𝜖1 − 𝛿1
𝑛 𝑇 ≃ −2𝜖1 .
𝑖 ≥ 1.
① The standard consistency relation is broken by the GB coupling.
② The GB coupling may lead to a reduction of the tensor-to-scalar ratio.
ZK Guo, N. Ohta, S. Tsujikawa, PRD 75 (2007) 023520;
ZK Guo, D.J. Schwarz, PRD 80 (2009) 063523;
ZK Guo, D.J. Schwarz, PRD 81 (2010) 123520;
PX Jiang, JW Hu, ZK Guo, PRD 88 (2013) 123508.
4. 数据之间的不自洽
①
②
③
④
平静之下，暗潮汹涌。
Cepheid+SNeIa, discrepant at the 2.5 σ level
SNLS, discrepant at the 2 σ level
cosmic shear, discrepant at the 2 σ level,
galaxy cluster, discrepant at the 3 σ level,
5. CMB温度涨落的反常
(1) the quadrupole-octopole alignment
(2) power deficit at low-l
(3) parity asymmetry
(4) hemispherical asymmetry
(5) the cold spot
……
(1) the quadrupole-octopole alignment
∆𝑇(𝑛)
=
𝑇
𝑎𝑙𝑚 =
𝑎𝑙𝑚 𝑌𝑙𝑚 (𝑛)
𝑙𝑚
𝑑𝑛𝑌𝑙𝑚 ∗ (𝑛)
𝑚2 𝑎𝑙𝑚 (𝑛)
𝑚
2
∆𝑇(𝑛)
𝑇
(2) power deficit at low-l
𝑎𝑙𝑚 ∗ 𝑎𝑙′ 𝑚′ = 𝛿𝑙𝑙′ 𝛿𝑚𝑚′ 𝐶𝑙
𝑎𝑙𝑚 =
∆𝑇(𝑛1 ) ∆𝑇(𝑛2 )
𝐶 𝜃 =
𝑇
𝑇
=
1
4𝜋
(2𝑙 + 1)𝐶𝑙 𝑃𝑙 (cos 𝜃)
𝑙
𝑑𝑛𝑌𝑙𝑚 ∗ (𝑛)
∆𝑇(𝑛)
𝑇
(3) parity asymmetry
𝑙
𝑃
+
𝑙 =
2
𝑛𝜋 𝑛(𝑛 + 1)
𝐶𝑛
2
2𝜋
sin2
𝑛𝜋 𝑛(𝑛 + 1)
𝐶𝑛
2
2𝜋
cos
𝑛=2
𝑙
𝑃− 𝑙 =
𝑛=2
𝑃+ (𝑙)
𝑔 𝑙 = −
𝑃 (𝑙)
(4) hemispherical asymmetry
the CMB temperature sky maps is modeled as
d 𝑛 = 1 + 𝐴 𝑝 ∙ 𝑛 s 𝑛 + n(𝑛)
 a super-horizon perturbation
the Sachs-Wolfe effect
𝛿𝑇 1
1
≃ Φ = ℛ (matter−dominated)
𝑇
3
3
𝒫ℛ 𝑘 =
𝐻
2
𝜙
𝐻
2𝜋
2
𝑘=𝑎𝐻
𝛿𝜙(𝑡∗ ) ⟶ 𝛿𝑘(𝑡∗ )
the diploe modulation of curvature perturbation
𝒫ℛ
the asymmetry A is
1/2
𝑝∙𝒙
𝑘, 𝒙 = 1 + 𝐴
𝒫ℛ 1/2 𝑘
𝑥ls
𝑛ℛ − 1
𝐴 = (1 − 𝜖)
(𝑘𝐿 𝑥ls )𝒫ℛ,𝐿 1/2
2
For a single-field slow-roll inflation,
GZ effect ⟹ (𝑘𝐿 𝑥ls
𝐴 ~ 𝒪(10−4 )
1
)𝒫ℛ,𝐿 2
≲ 0.02
primordial power spectrum:
𝒫ℛ = 𝒫ℛ inf
𝐶1 =
2
−𝑖𝑘
𝜋
2ℋ
2ℋ0
0
𝑒 ℋ0 (1 − 2 −
𝑖)𝐻0
32ℋ0
𝑘
𝑘
2
𝐶2 =
𝑖𝑘
𝜋
2ℋ0 2 2ℋ0
ℋ
𝑒 0 (1 − 2 +
𝑖)𝐻0
32ℋ0
𝑘
𝑘
2
For the bounce inflation,
2
𝑘 𝐶1 − 𝐶2
𝜋
𝑘
ℋ0
(
)+(
+ 𝑖)𝐻1
2ℋ0
𝑘
(
𝑘
ℋ0
)+(
− 𝑖)𝐻1
2ℋ0
𝑘
2
2
(
2
𝑘
)
2ℋ0
𝑘
(
)
2ℋ0
𝑛ℛ − 1 ~ 3 , ϵ ~ 3 ⟹ 𝐴 ~ 0.06
ZG Liu, ZK Guo, YS Piao, PRD 88 (2013) 063539;
ZG Liu, ZK Guo, YS Piao, arXiv:1311.1599
6. BICEP2分析结果
“至于你信不信，我反正信了。”
 primordial gravitational wave?
cosmic string, Faraday rotation, cosmic birefringence,
reionization, …
 a tension with the Planck result 𝑟 < 0.11 (2𝜎)
a large running of scalar spectral index
 for slow-roll inflation
𝑟
1/4
16
𝑉 ~2.25 × 10 GeV
0.2
 What is the inflaton field?
1/4
Higgs field?
 challenge for slow-roll inflation with a large running
{𝑛𝑠 , 𝛼𝑠 , 𝑟, 𝑁}
 If confirmed by Planck, the next step is to detect the
tensor spectral index.
𝑟
𝑛 𝑇 = − , 𝑛 𝑇 = 0, 𝑛 𝑇 > 0
8
四、中国的CMB物理
• 研究组（引力、天文、高能）
– 模型
– 数据处理
– 模型参数的拟合
• 微波探测实验
– 参与、主导、等待
谢谢大家！