CMB与超标准宇宙学模型郭宗宽

非线性和引力及时间本质研讨会，宁波大学2014.12.17

内容• 宇宙微波背景辐射（CMB）物理起源• Planck之后的标准宇宙学模型• Planck之后的一些问题

Big Bang Universe

一 . CMB物理起源

Recombination

Compton scatteringnow400

𝛿𝑇 (�̂�)𝑇

10−5

Mather,Smoot1989

Wilson,Penzias1964

COBE 1989 4yr WMAP 2001 9yr Planck 2009 30mo

NASA: CMBPol

ESA: COrE

COBE WMAP9 Planck 2013

• Ground-based experiments

ACBAR, CBI, VSA, QUaD, … ACT, ACTPol (2013~) SPT, SPTpol (95,150GHz, 2012~2015), SPT-3G (2016~2019) BICEP1 (2006~2008), BICEP2 (150GHz, 2010~2012), BICEP3 (95GHz, 2016~) POLARBEAR (150GHz, 2012~2013), POLARBEAR-2 (95,150GHz, 2016~) GroundBIRD (145,220GHz, 2016~) QUBIC (r ~ 0.01, bolometer, interferometer)

• Balloon-borne experiments

BOOMRANG, MAXIMA, … EBEX (150,250,410GHz, 2012), EBEX6K (90,150,220,280GHz, 2018) SPIDER (94,150,280GHz, 2013/2015) PIPER (200,270,350,600GHz, 2015)

二 . Planck之后的标准宇宙学模型

1. 六参数标准宇宙学模型2. Planck对标准宇宙学模型的限制

Launched on 14 May 2009Work for 30 monthsComplete 5 full-sky surveysPlanck 2013 results released 20 Mar 2013, 31 papersPlanck 2013 results. XVI, cited by 2775 recordsPlanck 2014 results presented at a conference, 1-5 Dec 2014Planck 2014 results will be released before the end of 2014

http://www.cosmos.esa.int/web/planck

– 宇宙晚期的 4个参数：

– 宇宙早期的 2个参数：

1. 六参数标准宇宙学模型{Ω𝑏h2, Ω𝑐 h

2 ,𝜃𝑀𝐶 ,𝜏 }{𝐴𝑠 ,𝑛𝑠 }

𝒫𝑠 (𝑘 )=𝐴𝑠 ( 𝑘𝑘0)𝑛𝑠− 1

𝛿𝜙⟺𝛿𝑔𝜇𝜈⇔𝛿 𝑓 ⟺𝛿𝑇 ,𝑈 ,𝑄

V (ϕ)

ϕ

inflation

1981

reheating

2. Planck对标准宇宙学模型的限制

相比WMAP， Planck的优势：① high sensitivity

② wide frequency– Planck: 30,44,70,100,143,217,353,545,857 GHz– WMAP: 23,33,41,61,94 GHz

③ high resolution ~ 5′ (WMAP: 15′)

Planck WMAP9TT

“None of these models are favoured over the standard six-parameter ΛCDM cosmology.”

标准宇宙学手册

Ferrara_Dec1_16h30_Efstathiou_Cosmology.pdf

三 . Planck之后的一些问题

1. 宇宙晚期的膨胀历史– Cepheid+SNeIa对的测量– SNLS对的测量

2. 宇宙晚期的结构形成– Cluster对的测量– LSS weak lensing对的测量

3. 宇宙早期的原初扰动– Planck温度涨落的反常– Planck温度功率谱对的限制

– : Cepheid+8 SNeIa, discrepant at 2.5σ– : SNLS, discrepant at the 2σ level

1.宇宙晚期的膨胀历史

1

Planck Collaboration, “Planck 2013 results. XVI. Cosmological parameters”, arXiv:1303.5076.

RG Cai, ZK Guo, B Tang, Phys. Rev. D89 (2014) 123518.

about 1.4 discrepancy

2.宇宙晚期的结构形成

– : Planck galaxy cluster, discrepant at 3σ– : CFHTLenS cosmic shear, discrepant at 2σ

1σ

Planck Collaboration, “Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts”, arXiv:1303.5080.

JW Hu, RG Cai, ZK Guo, B Hu, JCAP 05 (2014) 020.

3.宇宙早期的原初扰动– Planck温度涨落的反常： power deficit at low-l,

hemispherical asymmetry, the quadrupole-octopole alignment, parity asymmetry, the cold spot

d (�̂�)= (1+ 𝐴�̂� ∙ �̂�) s (�̂�)+n (�̂�)

Planck Collaboration, “Planck 2013 results. XXIII. Isotropy and statistics of the CMB”, arXiv:1303.5083.

𝛿𝑇𝑇≃

13

Φ=13ℛthe Sachs-Wolfe effect

𝛿𝜙(𝑡∗)⟶𝛿𝑘(𝑡∗)

𝒫ℛ (𝑘)=(𝐻�̇� )2

( 𝐻2𝜋 )2

𝑘=𝑎𝐻

the diploe modulation of curvature perturbation𝒫ℛ1/2 (𝑘 , 𝒙 )=(1+𝐴 �̂� ∙ 𝒙

𝑥 ls)𝒫ℛ

1/2 (𝑘 )

the asymmetry A is

𝐴=(1 −𝜖)(𝑛ℛ−1 )

2(𝑘𝐿𝑥 ls)𝒫ℛ ,𝐿

1 /2GZ   effect⟹(𝑘𝐿𝑥 ls)𝒫ℛ ,𝐿

12≲ 0.02

For a single-field slow-roll inflation, 𝐴 𝒪(10¿¿− 4)¿

𝒫ℛ=𝒫ℛinf 2𝜋𝑘|𝐶1−𝐶2|

2bounce inflation:

(𝑛ℛ −1 ) 3 , ϵ 3⟹𝐴 0.06For the bounce inflation,

ZG Liu, ZK Guo, YS Piao, Phys. Rev. D88 (2013) 063539; ZG Liu, ZK Guo, YS Piao, EPJC 74 (2014) 3006 .

– Planck的温度功率谱对的限制

Planck Collaboration, “Planck 2013 results. XXII. Constraints on inflation”, arXiv:1303.5082.

𝑉 1/4 ( 𝑟0.01 )1/4

1016 GeV

∆𝜙 ( 𝑟0.002 )1 /2(𝑁 ∗60 )𝑀𝑝𝑙

Observable gravity waves imply inflation happened around the GUT scale.

Observable gravity waves imply super-Planckian field excursion.

ZK Guo, N. Ohta, S. Tsujikawa, Phys. Rev. D75 (2007) 023520; ZK Guo, D.J. Schwarz, Phys. Rev. D80 (2009) 063523; ZK Guo, D.J. Schwarz, Phys. Rev. D81 (2010) 123520.

𝑅2𝐺𝐵≡𝑅𝜇𝜈𝜌𝜎 𝑅

𝜇𝜈𝜌𝜎− 4𝑅𝜇𝜈𝑅𝜇𝜈+𝑅2 .

𝑆=∫𝑑4 𝑥√−𝑔 [ 12𝑅−𝜔2𝜕𝜇𝜙𝜕

𝜇𝜙−𝑉 (𝜙 ) − 12𝜉 (𝜙)𝑅2

𝐺𝐵 ] ,inflation with the Gauss-Bonnet coupling:

background equations in a spatially-flat FRW Universe:

.0)(12)3(

),2(442

,2426

22,,

222

322

HHHVH

HHHHH

HVH

introducing Hubble and GB flow parameters:

.1,ln

ln,4,

ln

ln, 11121 i

ad

dH

ad

d

H

H ii

ii

the slow-roll approximation: and

to first order in the slow-roll approximation

.

82

,28

,2

221

1

11

11

21211

rn

r

n

t

s

a) The scalar spectral index contains not only the Hubble but also GB flow parameters.

b) The degeneracy of standard consistency relation is broken.

c) the horizon-crossing time 2/~)/ln(~ 1st ccN

PX Jiang, JW Hu, ZK Guo, Phys. Rev. D88 (2013) 123508.

chaotic inflation with an inverse power-law coupling

chaotic inflation with a dilaton-like coupling

3/4 00 V

.4

)1(16

,4

)2(21

nN

nr

nN

nns

𝑛𝑠− 1=−𝑛 (𝑛+2 )+𝛼𝜆𝑒−𝜆𝜙 𝜙𝑛+1 (2 𝜆𝜙−𝑛)

𝜙2

𝑟=8(𝑛−𝛼𝜆𝑒−𝜆𝜙𝜙𝑛+1)2

𝜙2

谢谢大家！