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2015年年终总结 郭宗宽
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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
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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
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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) “Higgs Inflation in Gauss-Bonnet Brane-World”, Rong-Gen Cai, ZKG, Shao-Jiang Wang, Phys. Rev. D92 (2015) “Reconstructing interaction between dark energy and dark matter using Gaussian Processes”, Tao Yang, ZKG, Rong-Gen Cai, Phys. Rev. D91 (2015) “Inflection point inflation and dark energy in supergravity”, Tie-Jun Gao, ZKG, Phys. Rev. D91 (2015) “Reheating Phase Diagram for Higgs Inflation”, Rong-Gen Cai, ZKG, Shao-Jiang Wang, Phys. Rev. D92 (2015) “Updated reduced CMB data and constraints on cosmological parameters”, Rong-Gen Cai, ZKG, Bo Tang, Int. J. Mod. Phys. D24 (2015)
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Inflationary magnetogenesis
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𝐵 1𝑀𝑝𝑐 ~ 10 −6 Gauss
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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
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Magnetic fields in intergalactic medium (voids)
𝐵≥ 10 −16 Gauss EW phase transition QCD phase transition Recombination epoch Inflationary magnetogenesis
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§ 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?
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§ 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
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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
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ℒ 𝐸𝑀 =− 1 4 𝑒 𝛼𝜙 𝐹 𝜇𝜈 𝐹 𝜇𝜈
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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
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§ 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
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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
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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 ~ , 𝐵 𝜆 ~ 10 −6 𝐻 𝐼 ~ 10 −12 Gauss
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The energy-momentum tensor is
The energy density is where The trace of i-j components is where
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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.
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2、将来研究工作的设想 中微子宇宙学 原初磁场的起源
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谢谢!
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