1. CMB的形成

Report
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:
 + − ↔  + 
Compton scattering:  +  − ↔  +  −
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
∆()
=

 =
  ()
∗
 
()
∆()


for a full sky, noiseless map
∗

′ ′ =  ′ ′

1
=
2 + 1

2

 cosmological parameter estimation
likelihood function for a full sky:
−2 ln ℒ =

th + 

(2 + 1) ln
+
−1
th

 + 
 CMB polarization
 raw timestreams (2010~2012)
Glitches and flux jumps are flagged.
 map making (T, Q, U)
  =   +   cos 2 +   sin 2
1 
=
 ± 
2
+
 =  
1  2 
−
=
−
2   2
±
( )
( )
 = cos 2 − cos 2
 = sin(2 ) − sin(2 )
detector transfer function, gain calibration, noise, beam function, polarization leakage, …
 from maps to power spectra
( ± )′  =  ∓2 ( ± ) 
 
=





 
=
Ω
∗

 



 +   =
2

2 
2

=
∗
Ω 2
  +  
−2

−2

=
∗
Ω −2
  −  

 −   =
−2




 
  =



 
  =





• rotationally invariant
• B has the opposite parity of T and E
• scalar modes contribute only to E
1 2
−2
= −  + 
2
 2
−2
= 
− 
2
1
=
2 + 1
1
 =
2 + 1
1
 =
2 + 1
1
 =
2 + 1

∗ 


9 data bandpowers: ∆l=35, 20<l<340


 = 

∗ 



∗ 


∗ 


 =

 direct likelihood
 bandpower likelihood
= vecp



model bandpowers by band window functions

 1/2

U
 
,


 cosmological parameter constraints









−1 
−2 log ℒ   =  ℳ′
′

D U†
 1/2

−1/2
U , D = eig 
−1/2
 
  = sign( − 1) 2( − ln − 1)
4. CMB各向异性的物理起源
• primary CMB anisotropies (at recombination)
inflation model (A.H. Guth in 1981)
 ⟺  ⇔  ⟺ , , 
• 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 
  =
2 2

  = 8
2
2
2




 −1

reconstruction of power spectrum
 parameterization:
•
•
•


ln   = ln  +  − 1 ln +  ln
0
0
2
+⋯
scale-invariant (As)
power-law (As, ns)
running spectral index (As, ns, as)
 ln ()
 ln 
 method:
ln () =
 advantages:
 ln ()
 ln 
ln



+ ln ( ) ,
ln   ,
cubic spline,

ln
+ ln ( ) ,

 < 
 ∈ { }
 <  < +1
 > 

• 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
 =  cos  − 
 =  cos  − 
 =  2 +  2
 =  2 −  2
 = 2  cos  − 
 = 2  sin  − 
scalar mode
tensor mode with  = 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
 2 = 2 + 2 + 2
 CMB anisotropies:
(1) the energy density
 = (1 + )−3/2  (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
 = (1 + )−3/2  (0)
(2) the weak reaction rate
Γ = 1 − 38 −
3(
4(
2
2
2
−  )
2
+ 3 )
 (1 + )−3/2 Γ (0)
 cosmological constraints:
data
the LIV parameter 
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:
=
 4  − 12 − 12   −   − 12() 2  ,
where  2  =   − 4  + 2 .
introducing Hubble and GB flow parameters:
1 = −

 ln 
 ln 
,

=
,

=
4
,

=
,
+1
1
+1
2
 ln 
 ln 
the predicted tensor-to-scalar ratio and spectral indices:
 ≃ 8 21 − 1 ,
21 2 − 1 2
 − 1 ≃ −21 −
,
21 − 1
  ≃ −21 .
 ≥ 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
∆()
=

 =
  ()

∗
 
()
2  ()

2
∆()

(2) power deficit at low-l
∗

′ ′ = ′ ′ 
∆(1 ) ∆(2 )
  =


=
1
4
(2 + 1)  (cos )

(3) parity asymmetry


+
 =
2
 ( + 1)

2
2
sin2
 ( + 1)

2
2
cos
=2

−  =
=2
+ ()
  ≡ −
 ()
(4) hemispherical asymmetry
the CMB temperature sky maps is modeled as
d  = 1 +   ∙  s  + n()
 a super-horizon perturbation
the Sachs-Wolfe effect
 1
1
≃ Φ = ℛ (matter−dominated)

3
3
  =

2


2
2
=
(∗ ) ⟶ (∗ )
the diploe modulation of curvature perturbation

the asymmetry A is
1/2
∙
,  = 1 + 
 1/2 
ls
 − 1
 = (1 − )
( ls ), 1/2
2
For a single-field slow-roll inflation,
GZ effect ⟹ ( ls
 ~ (10−4 )
1
), 2
≲ 0.02
primordial power spectrum:
 =  inf
1 =
2
−

2ℋ
2ℋ0
0
 ℋ0 (1 − 2 −
)0
32ℋ0


2
2 =


2ℋ0 2 2ℋ0
ℋ
 0 (1 − 2 +
)0
32ℋ0


2
For the bounce inflation,
2
 1 − 2


ℋ0
(
)+(
+ )1
2ℋ0

(

ℋ0
)+(
− )1
2ℋ0

2
2
2
(

)
2ℋ0

(
)
2ℋ0
 − 1 ~ 3 , ϵ ~ 3 ⟹  ~ 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  < 0.11 2
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?
 1/4
1/4
16
② for slow-roll inflation,  ~2.25 × 10 GeV
0.2
③ challenge for slow-roll inflation with a large running
{ ,  , , }
Step 5: if confirmed by Planck, the tensor spectral index
① scale-invariant tensor spectrum   = 0
② the standard consistency relation?   = −/8
③ blue spectrum?   > 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!

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