POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY

Transcription

1 POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY LOUIS YANG ( 楊智軒 ) UNIVERSITY OF CALIFORNIA, LOS ANGELES (UCLA) DEC 27, 2016 NATIONAL TSING HUA UNIVERSITY

2 OUTLINE Big Bang Cosmology Inflation Cosmological Horizon Brief History of the Early Universe Quantum Fluctuations The Higgs Potential Metastable of Our Vacuum Higgs Relaxation Matter-Antimatter Asymmetry 2

3 BIG BANG COSMOLOGY ds 2 = dt 2 a 2 (t)dx 2 CMB z 1100 Reionization z 10 z~0.3 now Big Bang? z~3400 Radiation Domination (Photons) Matter Domination (Dark Matter) Dark Energy Domination ρ T 4 a 4 size time p = 1 3 ρ a t 1/2 H = 1/2t ρ a 3 p = 0 a t 2/3 H = 2/3t ρ const. p = ρ 3

4 THE HORIZON PROBLEM Our universe is very homogeneous and isotropic. δδ T ~ ,000 years 300,000 years CMB Temperature map from Planck 4

5 SHORTCOMINGS OF THE BIG BANG COSMOLOGY 1. Large-scale Smoothness δδ T ~ Very flat Ω K < Scale invariant spectrum for Small-scale structure. 4. Unwanted relics: GUT predict Magnetic monopoles. Why don t see any? 5

6 INFLATION A period in the early universe that the space expands very fast a t e t H I H I : Hubble parameter a a = H I is constant. Everything is diluted extremely fast! A Horizon appears at a fixed distance. Matter Domination Radiation Domination Reheating Inflation size time 6

7 COSMOLOGICAL HORIZON Distance to the Horizon: l H ~ H 1 Horizon Beyond the horizon, star light haven t reach us yet. Matter or Radiation domination: H 1 Hubble rate decreases H 1/t Horizon size increases with time Stars go inside the horizon. 7

8 COSMOLOGICAL HORIZON Inflation: Hubble rate H I fixed Horizon size fixed Particle moved outside the horizon Horizon H I 1 Like surrounding by a backhole horizon 8

9 INFLATION A small patches of the universe which is in causal contact can expand to the size of current observable universe. Observable universe Horizon N 60 Inflation Horizon After Inflation e 60 Patch of Universe in thermal equilibrium Patch of Universe expands Rad. and Matter periods Homogeneous Universe 9

10 EVOLUTION OF INFLATON I Need vacuum energy domination period: Inflaton I t dd I I + 33I + = 0 dd 1. Slow Rolling of I I dd/dd and I 2 V 3HI dominates ρ V I constant 2. Coherent oscillations V(I) Coherent Oscillations Slow-Roll V~ 1 2 m I 2 I 2 Matter-like Λ I I 10

11 BRIEF HISTORY OF EARLY UNIVERSE 1. Inflation: Slow-rolling regime a t exp (t H I ) Temperature T 0 size Inflation Reheating Radiation Domination Matter Domination 2. Reheating: time Coherent oscillations Matter domination H 2/3t Inflaton decays Temperature increases 3. Radiation domination 11

12 QUANTUM FLUCTUATION QM: Vacuum is not empty! Quantum fluctuation even for ground state. P(ϕ) V(ϕ) φ They are only virtual particles in flat space. But becomes real during Inflation. 12

13 QUANTUM FLUCTUATION DURING INFLATION During inflation, quantum fluctuations get amplified. They becomes classical when the wavelength exits the horizon. φ(t) is doing like Brownian motion Horizon Horizon φ(x) Quantum fluctuation Inflation φ 0 0 Becomes classical 13

14 QUANTUM FLUCTUATION DURING INFLATION Quantum fluctuation can bring the field to non-zero value. But classical rolling down requires very long time (slowrolling). (Remember the 3HI term) A non-zero VEV of the scalar field is building up. V(ϕ) Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). ϕ min Quantum Jump Can t Roll Down Classically ϕ 14

15 QUANTUM FLUCTUATION AS THE SEED Fluctuation in the inflation field: δi H I 22 independent of wavelength k. Scale invariant spectrum Field fluctuation turns into Density fluctuations: δδ ρ V V δδ during reheating. Becomes seeds of structure formation 15

16 QUANTUM FLUCTUATION FOR OTHER FIELDS Massless field: φ 0 = φ 2 H I 22 N N: number of e-fold of inflation V(ϕ) Massive case V φ = 1 2 m2 φ 2 : φ 0 For V(φ) = λ 4 φ4 : 2 3 H I 8π 2 m φ H I /λ 1/4 ϕ min Quantum Jump Roll Down Classically ϕ In general: V φ 0 ~ H I 4 16

17 THE HIGGS BOSON In 2012, LHC has found the Higgs boson. V Φ = m 2 Φ + Φ + λ Φ + Φ, where Φ = v + h. Higgs boson mass: M h = ± ± GeV. A small λ μ = M t M 2 h 2v V(φ) v h Electroweak Vacuum φ C. Patrignani et al.(particle Data Group), Chin. Phys. C, 40, (2016). 17

18 RUNNING OF λ J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv: [hep-ph] QFT: Coupling constants changes with energy scale μ Needs RGE If no new physics, λ h becomes very small and turns negative at μ GeV. Figure from D. Buttazzo et al., arxiv: [hep-ph] 18

19 THE HIGGS EFFECTIVE POTENTIAL Another minimum in the potential: Planckain vacuum!! Much lower than the electroweak vacuum. QM: Our universe can tunnel to the Planckain vacuum Our universe might end in a big crunch! ssss V lll V φ Planckian Vacuum h lll φ Our Electroweak Vacuum ~ GeV h 19

20 METASTABLE OF OUR VACUUM J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv: [hep-ph] Our universe is right on the meta-stable region. 20

21 LARGE HIGGS VEV DURING INFLATION Higgs has a shallow potential at large scale. Large Higgs vacuum expectation value (VEV) during inflation. For V(φ) = λ 4 φ4 : φ H I /λ 1/4 For inflationary scale Λ I = GeV, the Hubble rate H I = Λ 2 I ~10 11 GeV, and λ~0. 00, the Higgs VEV after 3M pp inflation is φ 0 ~ GeV. For such a large VEV, the scalar field can be sensitive to higher dimensional operators. 21

22 POST-INFLATIONARY HIGGS RELAXATION During reheating, the Higgs field relaxes and oscillates. Amplitude decreases due to the Hubble friction. dd φ, T φ + 33φ + dφ = 0 Relaxation time 4 3 1/3 t rrr ~ T RR trr or t rrr ~ 7 λ 1 4 φ 0 Happens during reheating Breaks time reversal symmetry, and is out of thermal equilibrium. An important epoch! 22

23 MATTER-ANTIMATTER ASYMMETRY In 1928, Paul Dirac wrote down the Dirac equation, and predict the existence of anti-particle. Fundamental theory of particle physics seems symmetric between particle and anti-particle. We only see matter (baryons) in our universe. CMB observations: η B = n B n B n γ Baryogenesis: Doesn t work quite well. Leptogenesis: Make the lepton asymmetry first. Then later turns them into baryon asymmetry by Sphaleron process. 23

24 SAKHAROV CONDITIONS Andrei D. Sakharov (1967) Successfully Baryo- / Lepto-genesis requires: 1. Deviation from thermal equilibrium Post-inflationary Higgs relaxation 2. C (Charge) and CC (Charge & Parity) violations CC phase in the quark sector, higher dimension operator, 3. Baryon or Lepton number violation Right-handed Majorana neutrino 24

25 O 6 OPERATOR Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O 6 = 1 Λ n 2 μ φ 2 μ j B+L or O 5 = 1 Λ n μ μ φ j B+L Effective chemical potentials for baryon and lepton number μ eff, 6 = 1 Λ n 2 t φ 2 or μ eff, 5 = 1 Λ n t φ Shifts the energy levels between fermions and anti-fermions. V(ϕ) Reheating l, q Scalar VEV Rolls Down ϕ Leads to l, q 25

26 MAJORANA NEUTRINO Last ingredient: Right-handed neutrino N R with Majorana mass term M R. Motivated by the seesaw mechanism! The processes for ΔΔ = 2: ν L h 0 ν L h 0 ν L ν L h 0 h 0 ν L ν L h 0 h 0 26

27 EVOLUTION OF LEPTON ASYMMETRY LY, Pearce, Kusenko Phys. Rev. D92 (2015) Λ I = GeV, Γ I = 10 8 GeV, T RR = GeV, and φ 0 = GeV. For μ eff M n 2 case, choose M n = GeV. Could be the origin of matter-antimatter asymmetry! 27

28 SUMMARY Inflation provides a good solution to the horizon problem, and explain why the universe is so homogeneous. Quantum fluctuation of inflaton also provides the seed for structure formation. Our electroweak vacuum might not be the true vacuum. Our universe is now right on the meta-stable region. Higgs obtains large vacuum expectation during inflation. The relaxation of the Higgs VEV might be the origin of matter-antimatter asymmetry. Higgs relaxation is an important epoch in the early universe. Thanks for your listening! 28