宇宙磁场的起源 郭宗宽 2016两岸粒子物理及宇宙学研讨会 2016.7.4-7 P. Qian, Z.K. Guo, Phys. Rev. D 93, 043541 (2016) [arXiv:1512.05050] 宇宙磁场的起源 郭宗宽 2016两岸粒子物理及宇宙学研讨会 2016.7.4-7

内容提纲 §宇宙磁场的探测 §大尺度磁场的观测限制 §天体物理过程对磁场的放大 §原初磁场的产生机制

§宇宙磁场的探测 𝐵 galaxy ~ 𝐵 cluster ~ 10 −6 Gauss 𝐵 void ≥ 10 −16 Gauss Evidences: Magnetic fields are ubiquitous in our Universe. They are detected in astronomical structures of different sizes, from stars up to galaxies, galaxy clusters and voids. Methods: (1) Faraday rotation, (2) Zeeman splitting, (3) deflections of TeV gamma rays, (4) …… 𝐵 galaxy ~ 𝐵 cluster ~ 10 −6 Gauss 𝐵 void ≥ 10 −16 Gauss

optical/infrared extragalactic background light TeV gamma-rays optical/infrared extragalactic background light  electron positron pairs CMB photons  cascade gamma-rays Magnetic fields outside galaxies and galaxy clusters (Fermi/LAT) EW QCD Inflation Recombination 𝐵≥ 10 −16 Gauss Phys.Rev.D80:123012,2009 [arXiv:0910.1920]

§大尺度磁场的观测限制 CMB (Planck Collaboration, arXiv:1502.01594) energy momentum tensor Faraday rotation magnetically-induced bispectra breaking of statistical isotropy BBN (B. Cheng et al, arXiv:astro-ph/9606163) increasing the weak reaction rates increasing the electron density increasing the expansion rate of the universe 𝐵 1Mpc <4.4× 10 −9 Gauss 𝐵 1Mpc <2.8× 10 −9 Gauss 𝐵 BBN < 10 −6 Gauss

§天体物理过程对磁场的放大 Dynamo amplification mechanism (Y.B. Zeldovich et al, 1980) tiny seed magnetic fields ≳ 10 −13 G galactic dynamo galactic magnetic fields ~1𝜇 G

§原初磁场的产生机制 —— 宇宙相变 EW phase transition [C.J. Hogan, Phys. Rev. Lett. 51 (1983) 1488] QCD phase transition [J.M. Quashnock et al, ApJ 344 (1989) L49] (1) strength of magnetic fields, 𝐵 (2) correlation length, 𝜆 𝐵 𝜆 𝐵 ≤ 𝑎 0 𝑎 ∗ 𝐻 ∗ −1 ~ 10 −4 100 Gev 𝑇 ∗ pc

§原初磁场的产生机制 —— 宇宙暴涨 Models Problems breaking of conformal invariance (1) strong coupling problem (2) back reaction problem (3) curvature perturbation problem breaking of conformal invariance amplified fluctuations

Cited by: 578 records ℒ 𝐸𝑀 =− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 −𝑏𝑅 𝐴 𝜇 𝐴 𝜇 −𝑐 𝑅 𝜇𝜈 𝐴 𝜇 𝐴 𝜈 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

Cited by: 502 records ℒ 𝐸𝑀 =− 1 4 𝑒 𝛼𝜙 𝐹 𝜇𝜈 𝐹 𝜇𝜈

Cited by: 145 records ℒ 𝐸𝑀 =− 1 4 𝐼 2 (𝜙) 𝐹 𝜇𝜈 𝐹 𝜇𝜈 ❶ strong coupling problem ❷ back reaction problem ❸ curvature perturbation problem 𝐴 𝜇 → 𝑔𝐴 𝜇 ℒ=− 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 +𝑖 𝜓 𝛾 𝜇 ( 𝜕 𝜇 +𝑖𝑔 𝐴 𝜇 )𝜓 ℒ=− 1 4 𝑔 2 𝐹 𝜇𝜈 𝐹 𝜇𝜈 +𝑖 𝜓 𝛾 𝜇 ( 𝜕 𝜇 +𝑖 𝐴 𝜇 )𝜓 (1) 𝐼>1 during inflation, 𝐼~1 at the end of inflation (2) 𝜌 𝐸𝑀 < 𝐻 𝐼 2 during inflation (3) 𝜁 𝐸𝑀 < 𝐴 𝑠

§原初磁场的产生机制 —— 模型 Our action the equation of motion in 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 𝜒 2 𝐴 𝑘 ′′ + 2 𝑓 ′ 𝑓 𝐴 𝑘 ′ + 𝑘 2 𝐴 𝑘 =0 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

❶ the strong coupling problem Assuming 𝑓 𝜂 = 𝑓 𝑒 𝑎 𝑎 𝑒 𝑛 , requiring 𝑓 𝑒 ~1 and 𝑛<0 𝑣 𝑘 𝜂 = 1 2𝑘 𝑒 −𝑖𝑘𝜂 For short waves For long waves 𝑣 𝑘 𝜂 = 𝐶 1 𝑎 𝑛 + 𝐶 2 𝑎 −𝑛−1 If −1/2<𝑛<0, the first term dominates (a strong blue spectrum). If 𝑛<−1/2, the second term dominates. 𝐴 𝑘 𝜂 = 1 𝜒 𝑓 𝑒 2𝑘 𝑎 𝐻 𝐼 𝑘 −𝑛−1 𝑎 𝑎 𝑒 −𝑛

The power spectrum of the magnetic fields is If 𝑛=−3, the spectrum is scale-invariant. the entropy conservation, 𝑎 0 / 𝑎 𝑒 ~ 𝐻 𝐼 / 𝑇 0 ~ 10 32 𝐻 𝐼 For 𝑛=−3 and 𝐻 𝐼 ~ 10 −6 , 𝑎 0 / 𝑎 𝑒 ~ 10 29 , 𝐵 𝜆 ~ 10 −12 Gauss

❷ the back reaction problem 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. The solution to the back reaction problem requires 𝑄 1 = 𝑄 3 =0 ❸ the curvature perturbation problem the evolution of the curvature perturbation on super-Hubble scales

谢谢！