1. 引力波 — 早期宇宙的探针
郭宗宽
第二届引力波天体物理学术研讨会

2. Barry C. Barish
Ron Drever, died
Rainer Weiss
Kip S. Thorne
GW PRL 116 (2016)
LVT PRX 6 (2016)
GW PRL 116 (2016)
GW PRL 118 (2017)
GW ApJ 851 (2017) L35
GW PRL 119 (2017)
GW PRL 119 (2017)
2016 Breakthrough Prize in Fundamental Physics
2016 Gruber Foundation Cosmology Prize
2016 Shaw Prize
2016 Kavli Prize in Astrophysics
2016 Harvey Prize
2017 Nobel Prize in physics
2017 Fudan-Zhongzhi Science Award

3. 2016年2月12日

5. 2017年10月3日

7. 2017年10月17日

9. Taiji/TQ
LISA
Credit: LSC

11. Fundamental physics with GWs
Cosmology with GWs
as a standard siren
origin of a stochastic GW background
Fundamental physics with GWs
speed of GWs
polarization of GWs
tests of general relativity
black hole physics
Astrophysics with GWs
国家自然科学基金重大项目“引力波相关物理问题研究”
课题1：引力波和宇宙演化
课题2：引力波和基础物理
课题3：数值相对论和引力建模
课题4：引力波和相对论天体物理

12. Cosmological Probes
GWs
our Universe
Sources & Background

13. CBC作为晚期宇宙探针 测量宇宙的膨胀历史

14. Sne -- 标准烛光
BAO -- 标准尺度
GW -- 标准汽笛

15. GW standard sirens as cosmological probes
Credit: Nature 551 (2017) 85

16. The time delays from strongly lensed GW + EM
𝐷 ∆𝑡 ( 𝑧 𝑑 , 𝑧 𝑠 )= 𝑐∆ 𝑡 𝑖𝑗 (1+ 𝑧 𝑑 )∆ 𝜙 𝑖𝑗
10 lensed GW+EM
K. Liao, X.L. Fan, X.H. Ding, M. Biesiada, Z.H. Zhu, Nature Communications 8 (2017) 1148

17. SGWB作为早期宇宙探针 揭示宇宙暴胀物理

19. GWs from CBC GWs from inflation stochastic long time
low frequency < 10 −15 Hz
CMB-B, PTA, IFO
probe early-Universe physics
GWs from CBC
a direction
short time
high frequency > 10 −9 Hz
IFO, PTA
probe later-Universe physics
Log(f)
16
14
12
10 8 6 4 2 2
Planck 2009

20. ~7𝜎
GWs produced during inflaiton
GWs produced during reheating/preheating

21. Credit: Planck Collaboration, arXiv:1502.02114
P.X. Jiang, J.W. Hu, Z.K. Guo, Phys. Rev. D88 (2013) ;
Z.K. Guo, D.J. Schwarz, Phys. Rev. D81 (2010) ;
Z.K. Guo, D.J. Schwarz, Phys. Rev. D80 (2009) ;
Z.K. Guo, N. Ohta, S. Tsujikawa, Phys. Rev. D75 (2007)

22. GWs produced during inflation to distinguish inflationary models
to determine the energy scale of inflation
GWs produced during reheating/preheating
to constrain inflationary models
to determine the reheating temperature
𝑉 1/4 ~ 𝑟 / GeV
Reheating Constraints to Inflationary Models, L. Dai, et al., PRL 2014
Reheating Phase Diagram for Higgs Inflation, R.G. Cai, Z.K. Guo, S.J. Wang, PRD 2015

23. reheating scenario 𝐿= 1 2 𝜕 𝜇 𝜙 𝜕 𝜇 𝜙−𝑉 𝜙
𝐿= 1 2 𝜕 𝜇 𝜙 𝜕 𝜇 𝜙−𝑉 𝜙
𝜕 𝜇 𝜒 𝜕 𝜇 𝜒− 1 2 𝑚 𝜒 2 𝜒 2 − 1 2 𝑔 2 𝜙 2 𝜒 2
+ 𝜓 𝑖 𝛾 𝜇 𝜕 𝜇 − 𝑚 𝜓 𝜓−ℎ𝜙 𝜓 𝜓
𝑉(𝜙)~ 1 2 𝑚 2 𝜙−𝜎 2
Γ 𝜙→𝜒𝜒 = 𝑔 4 𝜎 2 8𝜋𝑚
Γ 𝜙→𝜓𝜓 = ℎ 2 𝑚 8𝜋

24. preheating scenario Credit: Kofman, et al, PRD 1997 𝑉 𝜙 = 1 2 𝑚 2 𝜙 2
𝑉 𝜙 = 1 2 𝑚 2 𝜙 2
~ 𝑔 2 𝜙 2 𝜒 2
𝑞 ~ 𝑔 2 / 𝑚 2
narrow parametric resonance
(𝑞~0.1)
broad parametric resonance
(𝑞~200)

25. ℎ 𝑖𝑗 +3𝐻 ℎ 𝑖𝑗 − 1 𝑎 2 𝛻 2 ℎ 𝑖𝑗 = 2 𝑀 pl 2 𝑎 2 Π 𝑖𝑗 𝑇𝑇
𝑃 𝑇 = 𝐴 𝑇 𝑘 𝑘 ∗ 𝑛 𝑇
𝜌 GW = 𝑀 pl ℎ 𝑖𝑗 ℎ 𝑖𝑗
Ω GW = 1 𝜌 𝑐 𝑑 𝜌 GW 𝑑 ln 𝑘
During inflation (with/without sources)
During reheating/preheating

26. Right: 𝑣= 10 −2 𝑀 pl ， 𝑔 2 ~0.05
Left: 𝑣= 10 −5 𝑀 pl ， 𝑔 2 ~ 10 −14
PRD 1997
Credit: J. Garcia-Bellido, D.G. Figueroa, Phys. Rev. Lett. 98 (2007)

27. 𝑉 𝜙,𝜒 = 1 2 𝜇 2 𝜙 𝑔 2 𝜙 2 𝜒 2
𝑞≡ 𝑔 2 𝑀 pl 2 𝜇 2 =2× 10 6
Right: 𝜇= 10 −6 𝑀 pl
Left: 𝜇= 10 −18 𝑀 pl
Credit: R. Easther, J.T. Giblin Jr, E.A. Lim, Phys. Rev. Lett. 99 (2007)

28. Gravitational Waves from Oscillons with Cuspy Potentials
𝑉 𝜙 =𝜆 𝑀 pl 4−𝑝 𝜙 𝑝 , 𝑝=1,2/3, 2/5
J. Liu, Z.K. Guo, R.G. Cai, G. Shiu, Phys. Rev. Lett. 120 (2018)

29. Silverstein et al, arXiv:0803.3085, arXiv:0808.0706
Planck Collaboration, arXiv:
Brandenberger et al, arXiv:
𝛿 𝜙 𝑘 +3𝐻𝛿 𝜙 𝑘 + 𝑘 2 𝑎 2 + 𝑉 " (𝜙) 𝛿 𝜙 𝑘 =0

30. Lattice simulation 𝑡 0 𝑡 1 𝑡 𝑒 𝜙 𝑛 𝑥 ,𝑡 ,ℎ 𝑥 ,𝑡 ,𝑎(𝑡) 𝑁 3 =256×256×256𝐿 𝐿 𝐿
Staggered
leapfrog
algorithm
𝑡 0
𝑡 1
𝑡 𝑒
𝜙 𝑛 𝑥 ,𝑡 ,ℎ 𝑥 ,𝑡 ,𝑎(𝑡)
𝑁 3 =256×256×256
𝐿= 𝐻 −1

32. 谢谢！ Workshop on gravitational waves July 15-28, 2018 ITP-CAS, Beijing
谢谢！