普朗克卫星2015年的宇宙学结果 郭宗宽 Lunch seminar, ITP-CAS 2015.3.31

CMB各向异性的物理 𝛿𝜙⟺𝛿 𝑔 𝜇𝜈 ⇔𝛿𝑓⟺𝛿𝑇,𝑈,𝑄

CMB各向异性的探测 Ground-based experiments Balloon-borne experiments Space experiments VS Planck 2013 SPT 2008-2011

名称 地点 时间 状态 l 范围 频率 (GHz) 极化 ACBAR 南极 2001~2008 完成 60~2700 150,219,274 无 CBI 智利 2002~2008 300~3000 26~36 VSA 西班牙 2002~2004 130~1800 SPT 2007~ 进行中 650~9500 95,150,220 ACT 2008~ 500~10000 148,218,277 DASI 2001~2003 200~900 有 CAPMAP 美国 500~1500 40,100 QUaD 2005~2010 200~2000 100,150 BICEP 2006~2008 21~335 100,150,220 QUIET 2008~2010 60~3500 40,90 BICEP2 2009~2012 150 KECKArray 2010~ ABS 2011~ 25~200 145 POLARBEAR 2012~ 50~2000 90,150 SPTpol 501~5000 95,150 ACTpol 2013~ 225~8725 90,146 BICEP3 2016~ 计划中 -- 95 CLASS 40, 90, 150,220

气球探测实验 名称 地点 时间 状态 l 范围 频率 (GHz) 极化 MAXIMA 美国 1995,98,99 完成 50~700 150~420 无 BOOMERanG 南极 1997~2003 25~1025 90~420 有 EBEX 2012~ 进行中 25~1000 150,250,410 SPIDER 2013,2015 10~300 90,150,280 PIPER -- 2015~ 计划中 200,270,350,600 MAXIMA BOOMERanG

空间探测实验 名称 卫星发射 时间 状态 l 范围 频率 (GHz) 极化 COBE NASA 1989~1993 完成 2~40 31.5, 53, 90 无 WMAP 2001~2010 2~1200 23, 33, 41, 61, 94 有 Planck ESA 2009~ 进行中 2~2500 30,44,70,100~857 CMBPol -- 计划中 COrE COBE 1989 4yr WMAP 2001 9yr Planck 2009 29 mo HFI 48 mo LFI NASA: CMBPol ESA: COrE

粒子物理 宇宙学 19参数的标准模型 6参数的标准模型 超标准模型，新物理 弱简并 强简并 LHC 普朗克卫星 TeV 近普朗克能标 We know much but understand little.

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

Planck 2013 results I. Overview of products and results II. Low Frequency Instrument data processing III. LFI systematic uncertainties IV. LFI beams and window functions V. LFI calibration VI. High Frequency Instrument data processing VII. HFI time response and beams VIII. HFI photometric calibration and mapmaking IX. HFI spectral response X. HFI energetic particle effects: characterization, removal, and simulation XI. All-sky model of thermal dust emission XII. Diffuse component separation XIII. Galactic CO emission XIV. Zodiacal emission

XV. CMB power spectra and likelihood XVI XV. CMB power spectra and likelihood XVI. Cosmological parameters (Cited by 3259 records, i.e., very active) XVII. Gravitational lensing by large-scale structure XVIII. The gravitational lensing-infrared background correlation XIX. The integrated Sachs-Wolfe effect XX. Cosmology from Sunyaev-Zeldovich cluster counts XXI. Power spectrum and high-order statistics of the Planck all-sky Compton parameter map XXII. Constraints on inflation XXIII. Isotropy and statistics of the CMB XXIV. Constraints on primordial non-Gaussianity XXV. Searches for cosmic strings and other topological defects XXVI. Background geometry and topology of the Universe XXVII. Doppler boosting of the CMB: Eppur si muove XXVIII. The Planck Catalogue of Compact Sources XXIX. The Planck catalogue of Sunyaev-Zeldovich sources XXX. Cosmic infrared background measurements and implications for star formation XXXI. Consistency of the Planck data

Planck 2015 results I. Overview of products and results II. Low Frequency Instrument data processing III. LFI systematic uncertainties IV. LFI beams and window functions V. LFI calibration VI. LFI maps VII. High Frequency Instrument data processing: Time-ordered information and beam processing VIII. HFI data processing: Calibration and maps IX. Diffuse component separation: CMB maps X. Diffuse component separation: Foreground maps XI. CMB power spectra, likelihood, and consistency of cosmological parameters XII. Simulations

XIII. Cosmological parameters (Cited by 96 records) XIV XIII. Cosmological parameters (Cited by 96 records) XIV. Dark energy and modified gravity XV. Gravitational lensing XVI. Isotropy and statistics of the CMB XVII. Primordial non-Gaussianity XVIII. Background geometry and topology of the Universe XIX. Constraints on primordial magnetic fields XX. Constraints on inflation XXI. The integrated Sachs-Wolfe effect XXII. A map of the thermal Sunyaev-Zeldovich effect XXIII. Thermal Sunyaev-Zeldovich effect–cosmic infrared background correlation XXIV. Cosmology from Sunyaev-Zeldovich cluster counts XXV. Diffuse, low-frequency Galactic foregrounds XXVI. The Second Planck Catalogue of Compact Sources XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources XXVIII. The Planck Catalogue of Galactic Cold Clumps

Planck 2013 vs. Planck 2015 Planck 2013 Planck 2015 Data 15.5 months 29 months for HFI 48 months for LFI Systematic 4K cooler lines; calibration offset; beam; deglitching algorithm; et al. Spectra TT TT, TE, EE Large-scale +WP (2<l<49) +lowP (2<l<29) Likelihood CamSpec (50~2500) Plik (30~2500) Parameters 𝑛 𝑠 , 𝐻 0 , 𝜏

Planck2015之后的标准宇宙学手册

Polarization spectra are generally highly consistent with TT spectra.

01. 标准模型 — 物质密度参数 02. 标准模型 — 哈勃常数 03. 标准模型 — 再电离 04. 标准模型 — 声学尺度 05 01. 标准模型 — 物质密度参数 02. 标准模型 — 哈勃常数 03. 标准模型 — 再电离 04. 标准模型 — 声学尺度 05. 标准模型 — 物质密度扰动 06. 标准模型 — 原初曲率扰动的谱指标 07. 超标准模型 — 暗能量和修改引力 08. 超标准模型 — 原初引力波 09. 超标准模型 — 原初曲率扰动的功率谱性质 10. 超标准模型 — 同曲率扰动 11. 超标准模型 — 原初非高斯 12. 超标准模型 — 空间拓扑 13. 超标准模型 — 中微子的总质量和种类数 14. 超标准模型 — 原初氦合成 15. 超标准模型 — 暗物质湮灭 16. 超标准模型 — 原初磁场

1. 标准模型 — 物质密度参数 Planck 2013 TT+WP: Ω 𝑚 =0.315±0.017 Planck 2015 TT+lowP: Ω 𝑚 =0.315±0.013 SNLS compilation (473): 123 low-redshifts, 242 3yr-SNLS, 93 SDSS, 14 HST a 2σ discrepancy Ω 𝑚 =0.227 JLA sample (740): 118 low-redshifts, 239 3yr-SNLS, 374 SDSS-II, 9 HST disappear Ω 𝑚 =0.295±0.034

2. 标准模型 — 哈勃常数 𝐻 0 = 67.3±1.2 km s −1 Mp c −1 (Planck 2013 TT+WP) 𝐻 0 =(67.31±0.96) km s −1 Mp c −1 (Planck 2015 TT+lowP) Riess 2011: Cepheids+8 Sne Ia 𝐻 0 =(73.8±2.4) km s −1 Mp c −1 a 2.5σ discrepancy Efstathiou 2014: NGC 4258 𝐻 0 =(70.6±3.3) km s −1 Mp c −1 disappear RG Cai, ZK Guo, B Tang, Phys. Rev. D89 (2014) 123518.

3. 标准模型 — 再电离 𝜏= 0.089 −0.014 +0.012 , 𝑧 re =11.1±1.1 (Planck 2013 TT+WP) 𝜏=0.066±0.016 , 𝑧 re = 8.8 −1.4 +1.7 (Planck 2015 TT+lowP+lens) Fan 2006: the evolution of the inter-galactic Lyα opacity measured in the spectra of quasars 𝑧 re ≈6 significantly low

4. 标准模型 — 声学尺度 BAO measurements: 6dFGS (z=0.1), SDSS-MGS (z=0.57), BOSS-LOWZ (z=0.32), BOSS-CMASS (z=0.57), WiggleZ (0.44,0.60,0.73) 1𝜎 2𝜎 Planck 2015+lowP+lensing Lyα BAO measurements: the Lyα forest with quasars 𝑐 𝐻(2.34) 𝑟 drag =9.14±0.20 (Lyα BAO) a 2.7σ discrepancy 𝑐 𝐻(2.34) 𝑟 drag =8.586±0. 021 (Planck 2015 TT+lowP+lens)

5. 标准模型 — 物质密度扰动 𝜎 8 =0.829±0.012 (Planck 2013 TT+WP) 𝜎 8 =0.829±0.014 (Planck 2015 TT+lowP) LSS redshift space distortions: 6dFGS, SDSS, BOSS, WiggleZ LSS weak lensing: CFHTLenS X-ray/optical/SZ cluster counts: CPPP, MaxBCG, ACT/SPT/Planck Samushia 2014 Planck 2015 TT+lowP+lensing a 1.5σ discrepancy Beutler 2014b Chuang 2013

a strong discrepancy Planck 2015 lensing Planck 2015 TT+TE+EE+lowP JW Hu, RG Cai, ZK Guo, B Hu, JCAP 05 (2014) 020.

6. 标准模型 — 原初曲率扰动的谱指标 𝑛 𝑠 =0.9603±0.0073 (Planck 2013 TT+WP) 𝑛 𝑠 =0.9655±0.0062 (Planck 2015 TT+lowP) a 0.7σ shift a 5.6σ deviation from the scale-invariance, i.e., dynamical V (ϕ) 𝒫 𝑠 𝑘 = 𝐴 𝑠 𝑘 𝑘 0 𝑛 𝑠 −1 inflationary scenario since 1981 ϕ reheating

评论： 普朗克研究组终于可以脱离其他天文观测数据，独立分析宇宙学参数。 也正是非常精确的数据使得分析结果与其他天文观测之间的不一致突显出来。 这些不一致性暗含了，要么观测数据有未考虑的系统误差，要么标准模型并不能很好地描述宇宙的演化规律。

7. 超标准模型 — 暗能量和修改引力 Reliability of Type Ia SNe : 不相信 2011 Nobel Prize Cosmological principle: 不自然 LTB Dark energy: 不理解 Modified gravity: 不喜欢 𝑤=− 1.13 −0.14 +0.24 (95%, Planck 2013 TT+WP+BAO) 𝑤= −1.54 −0.50 +0.62 (95%, Planck 2015 TT+lowP) PCA, 4 bins

a 2.5σ deviation a 2.3σ deviation a 3σ departure 𝜌 𝜙 ′ +3ℋ 𝜌 𝜙 1+ 𝑤 𝜙 =𝛽 𝜌 𝑐 𝜙 ′ 𝜌 𝑐 ′ +3ℋ 𝜌 𝑐 =−𝛽 𝜌 𝑐 𝜙 ′ V(ϕ)= 𝑉 0 𝜙 𝛼 a 3σ departure 𝜂(𝑎,𝑘)≡ Φ Ψ − 𝑘 2 Ψ≡4𝜋𝐺 𝑎 2 𝜇 𝑎,𝑘 𝜌Δ scale-independent & dark-energy related

8. 超标准模型 — 原初引力波 𝑟 0.002 <0.12 (95%, Planck 2013 TT+WP) 𝑟 0.002 <0.10 (95%, Planck 2015 TT+lowP) 𝑟 0.002 <0.08 (95%, Planck 2015 TT+lowP+BKP) Is the BB mode a smoking gun? sclar mode ⟹𝑇𝑇,𝑇𝐸,𝐸𝐸; tensor mode ⟹𝑇𝑇,𝑇𝐸,𝐸𝐸,𝐵𝐵 In slow-roll inflationary scenarios: 𝑉 1/4 ~ 𝑟 0.01 1/4 10 16 GeV Observable gravity waves imply inflation happened around the GUT scale. ∆𝜙~ 𝑟 0.002 1/2 𝑁 ∗ 60 𝑀 𝑝𝑙 Observable gravity waves imply super-Planckian field excursion.

25P 17P

V(𝜙)= Λ 4 1− 𝜙 𝑝 𝜇 𝑝 (Hilltop) V(𝜙)= Λ 4 1+ cos 𝜙 𝑓 (Natural) V(𝜙)= Λ 4 1− 𝑒 − 2 𝜙/( 3𝛼 𝑀 𝑝𝑙 ) 2 (α attractors, 𝑅 2 /nonminimal for α=1) 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; PX Jiang, JW Hu, ZK Guo, Phys. Rev. D88 (2013) 123508.

𝐾=−3 ln 1+ Φ+ Φ + Φ+ Φ 4 3 , 𝑊=𝑚 Φ 3 +𝑎 𝑒 𝑖𝜃 Φ+𝑏 𝑉 𝜒 = 𝑚 2 9 4 𝜒 4 − 6 𝑎 sin 𝜃 𝜒 3 +3 3 𝑏−𝑎 cos 𝜃 𝜒 2 + 𝑎 2 −2 3 𝑎𝑏 cos 𝜃 TJ Gao, ZK Guo, arXiv:1503.05643.

9. 超标准模型 — 原初曲率扰动的功率谱性质 𝑑 𝑛 𝑠 𝑑 ln 𝑘 =−0.013±0.009 (Planck 2013 TT+WP) 𝑑 𝑛 𝑠 𝑑 ln 𝑘 =−0.0084±0.0082 (Planck 2015 TT+lowP) 𝑟=0 𝑟≠0 ZG Liu, ZK Guo, YS Piao, Phys. Rev. D88 (2013) 063539; ZG Liu, ZK Guo, YS Piao, EPJC 74 (2014) 3006.

Reconstruction of the potential: Reconstruction of the power spectrum: Simple parameterizations of the power spectrum: power- law with exponential cut-off, broken power-law, step-like, logarithmic oscillations, linear oscillations Reconstruction of the potential: Reconstruction of the power spectrum: a dip at 𝑘~0.002 Mp c −1 , around 𝑙~20−30 ZK Guo, D J. Schwarz, YZ Zhang, JCAP 08 (2011) 031; ZK Guo, YZ Zhang, JCAP 11 (2011) 032; ZK Guo, YZ Zhang, Phys. Rev. D85 (2012) 103519; B Hu, JW Hu, ZK Guo, RG Cai, Phys. Rev. D90 (2014) 023544 .

10. 超标准模型 — 同曲率扰动 Initial conditions: CDI, NDI, NVI Additional degrees of freedom during inflation: axion, curvaton Parameterization: 𝒫 ℛℛ , 𝑛 ℛℛ , 𝒫 ℐℐ , 𝑛 ℐℐ , 𝒫 ℛℐ , 𝑛 ℛℐ cos Δ(𝑘) = 𝒫 ℛℐ 𝒫 ℛℛ 𝒫 ℐℐ , 𝛽 𝑖𝑠𝑜 𝑘 = 𝒫 ℐℐ 𝒫 ℛℛ +𝒫 ℐℐ If Δ is scale-independent, 𝑛 ℛℐ = 1 2 ( 𝑛 ℛℛ + 𝑛 ℐℐ )

Uncorrelated axion CDI: 𝒫 ℛℐ =0, 𝑛 ℐℐ =1 Fully correlated curvaton CDI: cos Δ =1, 𝑛 ℐℐ = 𝑛 ℛℛ = 𝑛 ℛℐ Fully anticorrelated curvaton CDI: cos Δ =−1, 𝑛 ℐℐ = 𝑛 ℛℛ = 𝑛 ℛℐ

11. 超标准模型 — 原初非高斯 Optimal bispectrum estimators: KSW, binned, modal 𝑓 𝑁𝐿 𝑙𝑜𝑐𝑎𝑙 =2.7±5.8, 𝑓 𝑁𝐿 𝑒𝑞𝑢𝑖𝑙 =−42±75, 𝑓 𝑁𝐿 𝑜𝑟𝑡ℎ𝑜 =−25±39 (Planck 2013 T) 𝑓 𝑁𝐿 𝑙𝑜𝑐𝑎𝑙 =0.8±5.0, 𝑓 𝑁𝐿 𝑒𝑞𝑢𝑖𝑙 =−4±43, 𝑓 𝑁𝐿 𝑜𝑟𝑡ℎ𝑜 =−26±21 (Planck 2015 T+E) Optimal bispectrum estimators: KSW, binned, modal Foreground-cleaned maps: SMICA, SEVEM, NILC, Commander One of the most powerful tests of inflation: models with a non-standard kinetic term multiple-field models 𝐵 Φ 𝑒𝑞𝑢𝑖𝑙 𝑘 1 , 𝑘 2 , 𝑘 3 =6 𝐴 2 𝑓 𝑁𝐿 𝑒𝑞𝑢𝑖𝑙 − 1 𝑘 1 4− 𝑛 𝑠 𝑘 2 4− 𝑛 𝑠 +2 perm. − 2 𝑘 1 𝑘 2 𝑘 3 2 4− 𝑛 𝑠 /3 + 1 𝑘 1 (4− 𝑛 𝑠 )/3 𝑘 2 2(4− 𝑛 𝑠 )/3 𝑘 3 4− 𝑛 𝑠 +5perm. 𝐵 Φ 𝑜𝑟𝑡ℎ𝑜 𝑘 1 , 𝑘 2 , 𝑘 3 =6 𝐴 2 𝑓 𝑁𝐿 𝑜𝑟𝑡ℎ𝑜 − 3 𝑘 1 4− 𝑛 𝑠 𝑘 2 4− 𝑛 𝑠 +2 perm. − 8 𝑘 1 𝑘 2 𝑘 3 2 4− 𝑛 𝑠 /3 + 3 𝑘 1 (4− 𝑛 𝑠 )/3 𝑘 2 2(4− 𝑛 𝑠 )/3 𝑘 3 4− 𝑛 𝑠 +5perm. 𝐵 Φ 𝑙𝑜𝑐𝑎𝑙 𝑘 1 , 𝑘 2 , 𝑘 3 =2 𝑓 𝑁𝐿 𝑙𝑜𝑐𝑎𝑙 𝑃 Φ 𝑘 1 𝑃 Φ 𝑘 2 +2 perm. LF Li, RG Cai, ZK Guo, B Hu, Phys. Rev. D86 (2012) 044020 .

12. 超标准模型 — 空间拓扑 Ω 𝑘 =− 0.042 −0.048 +0.043 (95%, Planck 2013 TT+WP+highL) Ω 𝑘 =− 0.052 −0.055 +0.049 (95%, Planck 2015 TT+lowP) Simple topology: 𝑅 3 , 𝑆 3 , 𝐻 3 𝑆 3 at 2σ CL Ω 𝑘 𝑡 ≡− 𝑘 𝑎 2 𝐻 2 →0 (inflation) Non-trivial topology: 𝑇 3 The size of the fundamental domain ℛ 𝑖 ≥0.97 𝜒 𝑟𝑒𝑐 at 99% CL

13. 超标准模型 — 中微子的总质量和种类数 𝑚 𝜈 <0.23 eV (95%, Planck 2013 TT+WP+highL+BAO) 𝑚 𝜈 <0.21 eV (95%, Planck 2015 TT+lowP+BAO) Impact on CMB: early ISW effect, free streaming Dark radiation: 𝑁 eff =3.046 and ∑ 𝑚 𝜈 =0.06 eV in SM 𝜌 𝜈 = 𝑁 eff 7 8 4 11 4/3 𝜌 𝛾 𝑁 eff = 3.30 −0.51 +0.54 (95%, Planck 2013 TT+WP+highL+BAO) 𝑁 eff =3.15±0.46 (95%, Planck 2015 TT+lowP+BAO) 𝑁 𝑒𝑓𝑓 >0 at 10 to 17σ CL ZK Guo, QG Huang, RG Cai, YZ Zhang, Phys. Rev. D86 (2012) 065004 .

14. 超标准模型 — 原初氦合成 BBN prediction of the helium fraction: 𝜔 𝑏 , 𝑁 𝑒𝑓𝑓 𝑌 𝑃 𝐵𝐵𝑁 +SM 𝑌 𝑃 𝐵𝐵𝑁 + 𝑁 𝑒𝑓𝑓 +SM BBN prediction of the helium fraction: 𝜔 𝑏 , 𝑁 𝑒𝑓𝑓 Aver 2013 observational bounds: 𝑌 𝑃 𝐵𝐵𝑁 =0.2465±0.0097 Constraints from the Planck data: ZK Guo, JW Hu, Phys. Rev. D87 (2013) 123519 .

15. 超标准模型 — 暗物质湮灭 𝑑𝐸 𝑑𝑡𝑑𝑉 𝑧 =2𝑔 𝜌 𝑐𝑟𝑖𝑡 2 𝑐 2 Ω 𝑐 2 1+𝑧 6 𝑝 𝑎𝑛𝑛 𝑧 , 𝑝 𝑎𝑛𝑛 𝑧 ≡𝑓(𝑧) 𝜎𝑣 𝑚 𝜒 Effects on CMB: heating, ionizations, lyα excitations of the medium

The Planck exclude at 95% CL a thermal relic cross-section for cosmic-ray excesses 95% CL 𝑓 𝑒𝑓𝑓 =0.67 𝜎𝑣 ≈3× 10 −26 cm 3 s −1 𝑓 𝑒𝑓𝑓 =0.13 gamma-ray excesses The Planck exclude at 95% CL a thermal relic cross-section for 𝜒 𝜒 → 𝑒 + 𝑒 − , 𝑓 𝑒𝑓𝑓 ≈0.6, 𝑚 𝜒 ≤44 GeV 𝜒 𝜒 → 𝜇 + 𝜇 − , 𝑓 𝑒𝑓𝑓 ≈0.2, 𝑚 𝜒 ≤16 GeV 𝜒 𝜒 → 𝜏 + 𝜏 − , 𝑓 𝑒𝑓𝑓 ≈0.15, 𝑚 𝜒 ≤11 GeV

16. 超标准模型 — 原初磁场 𝐵 1𝑀𝑝𝑐 <4.1 nG (95%, Planck 2013 TT+WP) 𝐵 1𝑀𝑝𝑐 <4.4 nG (95%, Planck 2015 TT+lowP) Observations: 𝐵~1 nG in galaxies and galaxy clusters Magnetogenesis: strong coupling, backreaction, perturbations Effects of PMF on CMB: The energy momentum tensor of PMF source scalar, vector and tensor perturbations. PMF induce a Lorentz force on baryons modifying their evolution.

谢谢大家！