Recent Progress in CMB
郭宗宽
北京工业大学
2014.4.17
内容
一、宇宙学发展现状
二、CMB物理
三、CMB的最新进展
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, RSD, GC, WL), SNIa
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
recombination:
𝑝 + 𝑒− ↔ 𝐻 + 𝛾
Compton scattering: 𝛾 + 𝑒 − ↔ 𝛾 + 𝑒 −
decoupling during recombination
400 cm−3 now
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
isotropy
Hot big bang
23 GHz
 WMAP (Wilkinson Microwave Anisotropy Probe)
the second generation CMB experiment, launched
on 30 June 2001, 9 years
141°
foreground mask
33 GHz
41 GHz
61 GHz
94 GHz
14, 5, 8, 6, 2 papers, 6873 citations
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
Mar 2013, 29 papers,
1609 citations
CMB spectrum
 BICEP2 (Background Imaging of Cosmic Extragalactic Polarization)
experiment — evidence for primordial B-mode is first detected.
BICEP1 (2006-2008)
BICEP2 (2010-2012)
SPT
The Dark Sector Lab (DSL)
26 cm aperture
150 GHz
383.7 deg2
2010-2012
4 tiles
8×8 array of
detector pairs
antenna networks
band-defining filters
bolometers
scan strategy
“BICEP2 2014 I: Detection of B-mode Polarization at Degree Angular Scales”,
arXiv:1403.3985, cited by 153 records
“BICEP2 2014 II: Experiment and Three-year Data Set”, arXiv:1403.4302
 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
3. CMB的数据分析
 CMB temperature fluctuations
 time-ordered data
 CMB temperature sky map
~10−5
 for Gaussian random fluctuations, the statistical properties of the
temperature field are determined by the angular power spectrum
∆𝑇(𝑛)
=
𝑇
𝑎𝑙𝑚 =
𝑎𝑙𝑚 𝑌𝑙𝑚 (𝑛)
∗
𝑑𝑛 𝑌𝑙𝑚
(𝑛)
∆𝑇(𝑛)
𝑇
𝑙𝑚
for a full sky, noiseless map
∗
𝑎𝑙𝑚
𝑎𝑙′ 𝑚′ = 𝐶𝑙𝑇𝑇 𝛿𝑙𝑙′ 𝛿𝑚𝑚′
𝐶𝑙𝑇𝑇
1
=
2𝑙 + 1
𝑎𝑙𝑚
2
𝑚
 cosmological parameter estimation
likelihood function for a full sky:
−2 ln ℒ =
𝑙
𝐶𝑙th + 𝒩𝑙
𝐶𝑙
(2𝑙 + 1) ln
+
−1
th
𝐶𝑙
𝐶𝑙 + 𝒩𝑙
 CMB polarization
 raw timestreams (2010~2012)
Glitches and flux jumps are flagged.
 map making (T, Q, U)
𝑑 𝑡 = 𝑇 𝑛𝑡 + 𝑄 𝑛𝑡 cos 2𝜓𝑡 + 𝑈 𝑛𝑡 sin 2𝜓𝑡
1 𝐴
=
𝑑 ± 𝑑𝐵
2
+
𝑑 = 𝑇 𝑛𝑡
1 𝛼 2 𝛼𝛽
𝑑−𝛼
=
𝑑−𝛽
2 𝛼𝛽 𝛽 2
𝑑±
𝑄(𝑛𝑡 )
𝑈(𝑛𝑡 )
𝛼 = cos 2𝜓𝑡𝐴 − cos 2𝜓𝑡𝐵
𝛽 = sin(2𝜓𝑡𝐴 ) − sin(2𝜓𝑡𝐵 )
detector transfer function, gain calibration, noise, beam function, polarization leakage, …
 from maps to power spectra
(𝑄 ± 𝑖𝑈)′ 𝑛 = 𝑒 ∓2𝑖𝜓 (𝑄 ± 𝑖𝑈) 𝑛
𝑇 𝑛
=
𝑇
𝑇
𝑎𝑙𝑚
𝑇
𝑎𝑙𝑚
𝑌𝑙𝑚 𝑛
=
𝑑Ω
∗
𝑌𝑙𝑚
𝑇 𝑛
𝑛
𝑇
𝑙𝑚
𝑄 + 𝑖𝑈 𝑛 =
2
𝑎𝑙𝑚
2𝑌𝑙𝑚 𝑛
2
𝑎𝑙𝑚
=
∗
𝑑Ω 2𝑌𝑙𝑚
𝑛 𝑄 + 𝑖𝑈 𝑛
−2
𝑎𝑙𝑚
−2
𝑎𝑙𝑚
=
∗
𝑑Ω −2𝑌𝑙𝑚
𝑛 𝑄 − 𝑖𝑈 𝑛
𝑙𝑚
𝑄 − 𝑖𝑈 𝑛 =
−2𝑌𝑙𝑚
𝑛
𝑙𝑚
𝐸
𝑎𝑙𝑚
𝑌𝑙𝑚 𝑛
𝐸 𝑛 =
𝑙𝑚
𝐵
𝑎𝑙𝑚
𝑌𝑙𝑚 𝑛
𝐵 𝑛 =
𝐸
𝑎𝑙𝑚
𝐵
𝑎𝑙𝑚
𝑙𝑚
• rotationally invariant
• B has the opposite parity of T and E
• scalar modes contribute only to E
1 2
−2
= − 𝑎𝑙𝑚 + 𝑎𝑙𝑚
2
𝑖 2
−2
= 𝑎𝑙𝑚
− 𝑎𝑙𝑚
2
1
=
2𝑙 + 1
1
𝐶𝑙𝐸𝐸 =
2𝑙 + 1
1
𝐶𝑙𝐵𝐵 =
2𝑙 + 1
1
𝐶𝑙𝑇𝐸 =
2𝑙 + 1
𝐶𝑙𝑇𝑇
𝑇∗ 𝑇
𝑎𝑙𝑚
𝑎𝑙𝑚
9 data bandpowers: ∆l=35, 20<l<340
𝑚
𝒟𝑏𝑇𝑇
𝓓𝑏 = 𝒟𝑏𝑇𝐸
𝒟𝑏𝑇𝐵
𝐸∗ 𝐸
𝑎𝑙𝑚
𝑎𝑙𝑚
𝑚
𝐵∗ 𝐵
𝑎𝑙𝑚
𝑎𝑙𝑚
𝑇∗ 𝐸
𝑎𝑙𝑚
𝑎𝑙𝑚
𝒟𝑏𝑋𝑌 =
𝑚
 direct likelihood
 bandpower likelihood
= vecp
𝒟𝑏𝑇𝐵
𝒟𝑏𝐸𝐵
𝒟𝑏𝐵𝐵
model bandpowers by band window functions
𝑚
𝑓 1/2
𝓓𝑏
U𝑏
𝑋𝑌 𝑋𝑌
𝑤𝑏,𝑙
𝒟𝑙
𝑙
 cosmological parameter constraints
𝑋𝑏𝑇𝑇
𝑋𝑏𝐸𝐸
𝑋𝑏𝐵𝐵
𝑋𝑏𝑇𝐸
𝑋𝑏𝐸𝐵
𝑋𝑏𝑇𝐵
𝒟𝑏𝑇𝐸
𝒟𝑏𝐸𝐸
𝒟𝑏𝐸𝐵
−1 𝑋
−2 log ℒ 𝓓𝑏 𝓓𝑏 = 𝑋𝑐 ℳ𝑐𝑐′
𝑐′
𝑔
D𝑏 U𝑏†
𝑓 1/2
𝓓𝑏
−1/2
U𝑏 , D𝑏 = eig 𝓓𝑏
−1/2
𝓓𝑏 𝓓𝑏
𝑔 𝑥 = sign(𝑥 − 1) 2(𝑥 − ln𝑥 − 1)
4. CMB各向异性的物理起源
• primary CMB anisotropies (at recombination)
inflation model (A.H. Guth in 1981)
𝛿𝜙 ⟺ 𝛿𝑔𝜇𝜈 ⇔ 𝛿𝑓 ⟺ 𝛿𝑇, 𝑈, 𝑄
• secondary CMB anisotropies (after recombination)
①
②
③
④
thermal/kinetic Sunyaev-Zel’dovich effect
integrated Sachs-Wolf effect
reionization
weak lensing effect
 slow-roll inflationary model
V (φ)
reheating
inflation
φ
for slow-roll inflation, the primordial power spectra of scalar
and tensor perturbations:
1 𝐻
𝒫𝑠 𝑘 =
2𝜖 2𝜋
𝐻
𝒫𝑇 𝑘 = 8
2𝜋
2
2
𝑘
𝑎𝐻
𝑘
𝑎𝐻
𝑛𝑠 −1
𝑛𝑇
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 temperature fluctuations
gravity
pressure
The stronger the contraction, the higher these peaks should be. Acoustic
oscillations are frozen in at recombination.
 CMB polarization
A monochromatic electromagnetic
wave propagating in the z direction
has an electric field vector
𝐸𝑥 = 𝑎𝑥 cos 𝜔𝑡 − 𝜉𝑥
𝐸𝑦 = 𝑎𝑦 cos 𝜔𝑡 − 𝜉𝑦
𝐼 = 𝑎𝑥 2 + 𝑎𝑦 2
𝑄 = 𝑎𝑥 2 − 𝑎𝑦 2
𝑈 = 2𝑎𝑥 𝑎𝑦 cos 𝜉𝑥 − 𝜉𝑦
𝑉 = 2𝑎𝑥 𝑎𝑦 sin 𝜉𝑥 − 𝜉𝑦
scalar mode
tensor mode with 𝑟 = 0.22
三、CMB的最新进展
• 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.
六参数的ΛCDM模型
暴胀模型的限制
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


k
(l  1)l 1  l l 1    2l 151 h   2l 52    0l 16 h d ln f 0  0 ,
 2l  1
d ln q
 
 
gs
f ( x , q , )  f 0 (q )1   ( x , q , ) , f 0 (q ) 
,
1  exp( 1   q / T0 )
q

l  (1   )
  m 2 a 2  (1   )q 2
 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
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. 暴胀模型的限制
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 𝑅 2 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
𝑛𝑠 − 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.
3. 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,
4. 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
∗
𝑑𝑛 𝑌𝑙𝑚
(𝑛)
𝑚2 𝑎𝑙𝑚 (𝑛)
𝑚
2
∆𝑇(𝑛)
𝑇
(2) power deficit at low-l
∗
𝑎𝑙𝑚
𝑎𝑙′ 𝑚′ = 𝛿𝑙𝑙′ 𝛿𝑚𝑚′ 𝐶𝑙
∆𝑇(𝑛1 ) ∆𝑇(𝑛2 )
𝐶 𝜃 =
𝑇
𝑇
=
1
4𝜋
(2𝑙 + 1)𝐶𝑙 𝑃𝑙 (cos 𝜃)
𝑙
(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
𝒫𝑠 𝑘 =
𝐻
2
𝜙
𝐻
2𝜋
2
𝑘=𝑎𝐻
𝛿𝜙(𝑡∗ ) ⟶ 𝛿𝑘(𝑡∗ )
the diploe modulation of curvature perturbation
𝒫𝑠
the asymmetry A is
1/2
𝑝∙𝒙
𝑘, 𝒙 = 1 + 𝐴
𝒫𝑠 1/2 𝑘
𝑥ls
𝑛𝑠 − 1
𝐴 = (1 − 𝜖)
(𝑘𝐿 𝑥ls )𝒫𝑠,𝐿 1/2
2
For a single-field slow-roll inflation,
GZ effect ⟹ (𝑘𝐿 𝑥ls
𝐴 ~ 𝒪(10−4 )
1
)𝒫𝑠,𝐿 2
≲ 0.02
primordial power spectrum:
𝒫𝑠 = 𝒫𝑠 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
𝑛𝑠 − 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
5. BICEP2分析结果
Step 1: is the data reliable?
① some unknown sources of systematic error
② data analysis pipeline
“至于你信不信，我反正信了。”
③ likelihood method
Step 2: primordial gravitational wave?
①
②
③
④
cosmic string
Faraday rotation
cosmic birefringence
reionization
Step 3: a tension with the Planck result 𝑟 < 0.11 2𝜎
①
②
③
④
⑤
⑥
a large running of scalar spectral index
step potential
fast-slow-roll inflation
non-Bunch-Davis vacuum, false vacuum, trans-Planck
anti-correlated tensor-curvature
anti-correlated iso-curvature
Step 4: what is the inflation field?
① Higgs field?
𝑟 1/4
1/4
16
② for slow-roll inflation, 𝑉 ~2.25 × 10 GeV
0.2
③ challenge for slow-roll inflation with a large running
{𝑛𝑠 , 𝛼𝑠 , 𝑟, 𝑁}
Step 5: if confirmed by Planck, the tensor spectral index
① scale-invariant tensor spectrum 𝑛 𝑇 = 0
② the standard consistency relation? 𝑛 𝑇 = −𝑟/8
③ blue spectrum? 𝑛 𝑇 > 0
string gas cosmology
bounce inflation
super-inflation before slow-roll inflation
B Hu, JW Hu, ZK Guo, RG Cai, arXiv:1404.3690
谢谢大家！