2015年年终总结 郭宗宽 2015.12.22
1、2015年的工作情况及进展 组织学术会议 参加学术会议 The International Conference on Gravitation and Cosmology/The Fourth Galileo-Xu Guangqi Meeting 2015年5月4日―8日,中科院理论所,来自30多个国家的200多名学者参加了会议,其中包括国际相对论天体物理中心主任鲁菲尼、国际广义相对论学会前理事长阿什塔克等著名科学家。 参加学术会议
做学术报告 教学任务 基金申请 研究生培养 理论所,lunch seminar “引力理论与宇宙学国际会议”,大会报告 “中国物理学会2015年秋季学术会议”,分会报告 中科大、上交大、上大、华中科大等了6个专题报告 教学任务 中国科学院大学国际教育学院 《Lectures on frontiers in physics》 中国科学院大学研究生院雁西湖校区 《相对论天体物理》 基金申请 研究生培养
完成学术论文 “A model of inflationary magnetogenesis”, Peng Qian, ZKG, under review in Phys. Rev. D. “Null test of the cosmic curvature using H(z) and supernovae data”, Rong-Gen Cai, ZKG, Tao Yang, under review in Phys. Rev. D. “Principal component analysis of the reionization history from Planck 2015 data”, Wei-Ming Dai, ZKG, Rong-Gen Cai, Phys. Rev. D92 (2015) 123521. “Higgs Inflation in Gauss-Bonnet Brane-World”, Rong-Gen Cai, ZKG, Shao-Jiang Wang, Phys. Rev. D92 (2015) 063514. “Reconstructing interaction between dark energy and dark matter using Gaussian Processes”, Tao Yang, ZKG, Rong-Gen Cai, Phys. Rev. D91 (2015) 123533. “Inflection point inflation and dark energy in supergravity”, Tie-Jun Gao, ZKG, Phys. Rev. D91 (2015) 123502. “Reheating Phase Diagram for Higgs Inflation”, Rong-Gen Cai, ZKG, Shao-Jiang Wang, Phys. Rev. D92 (2015) 063506. “Updated reduced CMB data and constraints on cosmological parameters”, Rong-Gen Cai, ZKG, Bo Tang, Int. J. Mod. Phys. D24 (2015) 1550071.
Inflationary magnetogenesis
𝐵 1𝑀𝑝𝑐 ~ 10 −6 Gauss
Upper limits (Planck Collaboration, arXiv:1502.01594) the energy momentum tensor Faraday rotation magnetically-induced bispectra the breaking of statistical isotropy Planck 𝐵 1𝑀𝑝𝑐 <4.4× 10 −9 Gauss
Magnetic fields in intergalactic medium (voids) 𝐵≥ 10 −16 Gauss EW phase transition QCD phase transition Recombination epoch Inflationary magnetogenesis
§ Astrophysical processes dynamo mechanism (Y.B. Zeldovich et al, 1980s) tiny seed magnetic fields ≳ 10 −13 G galactic dynamo galactic magnetic fields ~1𝜇 G EW phase transition, QCD phase transition, inflation?
§ Inflationary magnetogenesis Models problems (1) strong coupling problem (2) back reaction problem (3) curvature perturbation problem ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 breaking of conformal invariance amplified vacuum fluctuations
ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 −𝑏𝑅 𝐴 𝜇 𝐴 𝜇 −𝑐 𝑅 𝜇𝜈 𝐴 𝜇 𝐴 𝜈 𝑈(1) ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 −𝑏𝑅 𝐹 𝜇𝜈 𝐹 𝜇𝜈 −𝑐 𝑅 𝜇𝜈 𝐹 𝜇𝜅 𝐹 𝜅 𝜈 −𝑑 𝑅 𝜇𝜈𝜆𝜅 𝐹 𝜇𝜈 𝐹 𝜆𝜅 ~ 10 −40 G ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 − 𝐷 𝜇 𝜙 ( 𝐷 𝜇 𝜙) ∗ ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 − 1 2 𝜕 𝜇 𝜃 𝜕 𝜇 𝜃+ 𝑔 𝑎 𝜃 𝐹 𝜇𝜈 𝐹 𝜇𝜈 Non-Gaussianity
ℒ 𝐸𝑀 =− 1 4 𝑒 𝛼𝜙 𝐹 𝜇𝜈 𝐹 𝜇𝜈
ℒ 𝐸𝑀 =− 1 4 𝐼 2 (𝜙) 𝐹 𝜇𝜈 𝐹 𝜇𝜈 ℒ=− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 +𝑖 𝜓 𝛾 𝜇 ( 𝜕 𝜇 +𝑖𝑔 𝐴 𝜇 )𝜓 𝐴 𝜇 → 𝑔𝐴 𝜇 ℒ=− 1 4 𝑔 2 𝐹 𝜇𝜈 𝐹 𝜇𝜈 +𝑖 𝜓 𝛾 𝜇 ( 𝜕 𝜇 +𝑖 𝐴 𝜇 )𝜓 ❶ strong coupling problem ❷ back reaction problem ❸ curvature perturbation problem 𝐼>1 during inflation, 𝐼~1 at the end 𝜌 𝐸𝑀 < 𝐻 𝐼 2 during inflation 𝜁 𝐸𝑀 < 𝐴 𝑠
§ A model of inflationary magnetogenesis our action the equation of motion a spatially-flat FRW metric 𝑑 𝑠 2 = 𝑎 2 (𝜂)(−𝑑 𝜂 2 +𝑑 𝑥 2 ) Coulomb gauge: 𝐴 0 =0 and 𝜕 𝑖 𝐴 𝑖 =0 Fourier expansion
normalization condition assuming normalization condition where 𝜒 2 = 𝑐 1 −4 12 𝑐 2 +3 𝑐 3 +2 𝑐 4 𝐻 𝐼 2 defining a new variable 𝑣 𝑘 =𝜒𝑓 𝐴 𝑘 𝜒 𝑣 𝑘 ′′ + 𝑘 2 − 𝑓′′ 𝑓 𝑣 𝑘 =0 assuming 𝑓 𝜂 = 𝑓 𝑒 𝑎 𝑎 𝑒 𝑛 ❶ solution to the strong coupling problem, requiring 𝑓 𝑒 ~1 and 𝑛<0
for short waves for long waves If −1/2<𝑛<0, the first term dominates. a strong blue spectrum If 𝑛<−1/2, the second term dominates. The power spectrum is a scale invariant spectrum for 𝑛=−3 the entropy conservation, for 𝐻 𝐼 ~ 10 −6 , 𝑎 0 / 𝑎 𝑒 ~ 10 29 , 𝐵 𝜆 ~ 10 −6 𝐻 𝐼 ~ 10 −12 Gauss
The energy-momentum tensor is The energy density is where The trace of i-j components is where
The main contribution to the energy density and pressure comes from the power spectrum of the electric fields. ❷ solution to the back reaction problem, requiring 𝑄 1 = 𝑄 3 =0 the evolution of the curvature perturbation on super-Hubble scales ❸ The curvature perturbation problem is avoided if 𝑄 1 = 𝑄 3 =0.
2、将来研究工作的设想 中微子宇宙学 原初磁场的起源
谢谢!