Postinflationary Higgs Relaxation and the Origin of Matter Louis Yang University of California, Los Angeles Ph.D. Final Oral Presentation May 16, 2017
Outline Motivation: the Higgs potential Quantum Fluctuation during inflation Postinflationary Higgs relaxation Leptogenesis via Higgs field relaxation Cosmic Infrared Background (CIB) excess Isocurvature perturbation Based on: [1] A. Kusenko, L. Pearce, LY, Phys. Rev. Lett. 114, 061302 (2015). [2] L. Pearce, LY, A. Kusenko, M. Peloso, Phys. Rev. D 92, 023509 (2015). [3] LY, L. Pearce, A. Kusenko, Phys. Rev. D 92, 043506 (2015). [4] H. Gertov, L. Pearce, F. Sannino, LY, Phys. Rev. D 93, 115042 (2016). [5] A. Kusenko, L. Pearce, LY, Phys. Rev. D 93, 115005 (2016). [6] M. Kawasaki, A. Kusenko, L. Pearce, LY, Phys. Rev. D 95, 103006 (2017). 2
Motivation The Higgs Potential 3
The Higgs Boson In 2012, ATLAS and CMS found the Higgs boson. V Φ = m 2 Φ + Φ + λ Φ + Φ 2, where Φ = 1 0 2 v + h. Higgs boson mass: M h = 111. 00 ± 0. 22 ± 0. 11 GeV. A mass smaller than expected! A small quartic coupling λ μ = M t M h 2 2v 2 0. 111 V(φ) v h Electroweak Vacuum φ C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016). 4
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:1307.3536 [hep-ph] QFT: Coupling constants changes with energy scale μ β λ = 33 44 2 y t 4 + Due to large top mass m t = 1 2 y tv If no new physics, λ h becomes very small and turns negative at μ 10 11 10 11 GeV. Figure from D. Buttazzo et al., arxiv:1307.3536 [hep-ph] 5
The Higgs Effective Potential Another minimum in the potential: Planckain vacuum!! Much lower than the electroweak vacuum. Our universe can tunnel into the Planckain vacuum and end in a big crunch! ssss V lll V φ Planckian Vacuum h lll φ Our Electroweak Vacuum ~10 10 10 12 GeV h 6
Meta-stability 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:1307.3536 [hep-ph] Our universe seems to be right on the meta-stable region. 7
The Higgs Effective Potential What does it imply? A shallow Higgs potential at large scale A large Higgs VEV during inflation ssss V lll V φ Planckian Vacuum h lll φ Our Electroweak Vacuum ~10 10 10 12 GeV 8
I Quantum Fluctuation during Inflation 9
Quantum Fluctuation during Inflation During inflation, quantum fluctuations get amplified. They becomes classical when the wavelength exits the horizon. φ(t) jumps randomly like Brownian motion. Horizon Horizon φ(x) Quantum fluctuation Inflation φ 0 0 Becomes classical 10
Quantum Fluctuation during Inflation Quantum fluctuation brings the field to non-zero value. Classical rolling down follows φ + 3H I φ = V φ, which requires t rrr ~ d2 V φ dφ 2 1 2 = 1 m φ If m φ H I, insufficient time to relax (slow-rolling). A non-zero VEV of the scalar field is building up. V(ϕ) ϕ min Quantum Jump Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Can t Roll Down Classically ϕ 11
Large VEV of Scalar Fields A. A. Starobinsky (1982) A. Vilenkin (1982) Fokker-Planck equation: P c φ,t = j c where j c = P c φ, t : probability distribution of φ H 3 P c 8π 2 + P c H Massless scalar, the field undergoes random walks φ 0 φ 2 H I 3 2 22 t = H I 22 Massive case V φ = 1 2 m2 φ 2 : φ 0 3 H I 8π 2 m For V(φ) = λ 4 φ4 : φ 0 0. 33H I /λ 1/4 In general, V φ 0 ~ H I 4 dd dd N, N: number of e-folds 2 12
Large Higgs VEV During Inflation Higgs has a shallow potential at large scale (small λ). Large Higgs vacuum expectation value (VEV) during inflation. For inflationary scale Λ I = 10 11 GGG, the Hubble rate Λ I 2 H I = ~10 11 GGG, and λ~0. 00, the Higgs VEV after 3M pp inflation is φ 0 0. 33H I /λ 1/4 ~ 10 11 GGG. For such a large VEV, the Higgs field can be sensitive to higher dimensional operators. 13
Postinflationary Higgs Field Relaxation 14
Post-inflationary Higgs Relaxation As the inflation end, the H drops. When H < m φ,eee, the Higgs field can relax classically φ t + 33 t φ t + V eff φ, T t = 0 φ V eee (φ, T) is the finite temperature effective potential. Higgs field oscillates with decreasing amplitude due to the Hubble friction. Relaxation time 2.5 4/3 1 t rrr = t RR if thermal mass dominates V a T T RR t α RR 2 T 2 T 2 φ 2 t rrr = 6. 9/ λφ 0 if the zero T dominates V λφ 4 /4 Typically during reheating or right after reheating. 15
Post-inflationary Higgs Relaxation M. Kawasaki, A. Kusenko, L. Pearce, LY, Phys. Rev. D 95, 103006 (2017). If the thermal mass dominates, V φ, T 1 2 α T 2 T 2 φ 2 where α T λ + 9 4 g2 + 3 4 g 2 2 + 3y t 11 0. 33 at μ = 10 11 GeV. The equation of motion is approximately A solution: φ t + 2 t φ t + α T 2 T RR 2 3 3 φ t = φ 0 Γ 5 2 3 J 2 3 where β = T RR t RR and x = t/t RR. 2 t t RR 4α T β 3 φ t = 0 4 x3 1 α T β 2 3 x 16
Post-inflationary Higgs Relaxation Thermal mass dominated Zero T potential dominated What can this do for us? Breaks time reversal symmetry, and provides the out of thermal equilibrium condition. An important epoch for the matter-antimatter asymmetry! 17
Initial Conditions for the Higgs field Initial Condition 1 (IC-1): A metastable Planckian vacuum due to higher dimensional operators O~ 1 1 1 M 2 φ6, M 4 φ8, φ11 M6 Higgs field trapped in a metastable vacuum during inflation Reheating destabilize the metastable vaccum via δδ~t 2 φ 2 and the Higgs VEV relaxes V(ϕ) H 4 Trapped Reheating Second Min. Thermal correction ϕ 18
Initial Conditions for the Higgs field Initial Condition 2 (IC-2): Inflaton VEV induced mass term to the Higgs via O = I n φ m /Λ n+m 4 V(ϕ) Large I during early stage of inflation Large Higgs mass and suppressing quantum φ 2 ~0 fluctuation In the last N e-fold of inflation, I decreases and Higgs becomes massless with H N φ 0 = 22 Last Early N e-folds stage End of of inflation Quantum jumps Rolls down classically φ 2 starts φ 2 to = grow H 2 I N/4π 2 H 4 H 4 ϕ 19
II Leptogenesis via the Relaxation of the Higgs Field 20
Sakharov Conditions Andrei D. Sakharov (1967) Successfully Leptogenesis requires: 1. Deviation from thermal equilibrium Post-inflationary Higgs relaxation 2. C and CC violations CC phase in the quark sector (not enough), higher dimensional operator, 3. Lepton number violation Right-handed Majorana neutrino, others 21
Effective Operator M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) CP violation: Consider the effective operator: O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB, W and B: SS 2 L and U 1 Y gauge fields W : dual tensor of W Λ n : energy scale when the operator is relevant In standard model, integrating out a loop with all 6 quarks: Also used by baryogenesis But suppressed by small Yukawa and small CC phase 22
Effective Operator O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB Replace the SM fermions by heavy states that carry SS 2 charge. Scale: Λ n = M n mass (must not from the SM Higgs) or Λ n = T temperature 23
Effective Chemical Potential Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB Using electroweak anomaly equation, we have O 6 = 1 2 Λ φ 2 μ μ j B+L, n μ where j B+L is the B + L fermion current. Integration by part: O 6 = 1 Λ n 2 μ φ 2 μ j B+L Similar to the one use by spontaneous baryogenesis. Breaks CPT spontaneously while φ is changing! Sakharov s conditions doesn t have to be satisfied explicitly in this form. 24
Effective Chemical Potential O 6 = 1 Λ n 2 μ φ 2 μ j B+L Effective chemical potential for baryon and lepton number: μ eff = 1 Λ n 2 t φ 2 Shifts the energy levels between fermions and anti-fermions while Higgs is rolling down (φ 0). V(ϕ) Scalar VEV Rolls Down Reheating Leads to l, q l, q ϕ 25
Lepton Number Violation Last ingredient: Right-handed neutrino N R with Majorana mass term M R. 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 For m ν ~0. 1 ev, σ R ~ Σ 2 im ν,i ~10 33 GeV 2. 2 111v EE LY, L. Pearce, A. Kusenko, Phys. Rev. D 92, 043506 (2015). 26
Evolution of Lepton Asymmetry Boltzman equation: n L + 33n L 2 π 2 T3 σ R n L 2 π 2 μ eeet 2 Final lepton asymmetry: Y = n L s 99σ R π 6 g S φ 0 Λ n 2 3z0 T RR 8+ 11 eee 4α T t RR π 2 Λ I = 1. 5 10 11 GeV, Γ I = 10 8 GeV, T RR = 5 10 11 GeV, φ 0 = 6 10 11 GeV. For μ eff M n 2 case, M n = 5 10 11 GeV. σ R T 3 RR t RR Could be the origin of matter-antimatter asymmetry! 27
Leptogenesis via other scalar fields Elementary Goldstone Higgs (EGH) σ H. Gertov, L. Pearce, F. Sannino, and LY Phys. Rev. D 93, 115042 (2016), arxiv:1601.07753 [hep-ph] Axion a A. Kusenko, K. Schmitz, T. Yanagida, PRL 115, 011302 (2015) Pseudoscalar S L λ γ α 111v EE SF μμ F μμ Sign of S determines the sign of baryon asymmetry Domain wall Fixed by large correlation length A. Kusenko, L. Pearce, and LY Phys. Rev. D 93, 115005 (2016), arxiv:1604.02382 [hep-ph]. 28
Leptogenesis via the Neutrino Production L. Pearce, LY, A. Kusenko, M. Peloso, PRD 92, 023509 (2015) Evolving background scalar field creates particles Initial vacuum is not the vacuum at a later time Time-dependent background mixes positive and negative frequency solutions. Neutrino production via Higgs relaxation L = Y e L i j ii Φe R ν Yii L i j 1 Φ N R 2 M iin i j R N R + h. c. With effective chemical potential and Majorana mass term, the system favors production of neutrinos over antineutrinos. Work better at low reheat temperature ( T RR ~ Γ I m pp ) -> less dilution by entropy production of inflaton decay. 29
III Cosmic Infrared Background Radiation excess 30
Cosmic Infrared Background (CIB) fluctuations CIB: IR part of extragalactic background light from galaxies at all redshifts Difficult to determine absolute intensity (isotropic flux) More focus on the anisotropies (spatial fluctuation) of CIB CIB (spatial) fluctuations observed by Spitzer space telescope 31
Excess in the CIB fluctuations Helgason et al., MNRAS 455, 282 (2015) Kashlinsky et al. ApJ 804, 99 (2015) Spitzer AKARI Excess found in near-ir (1 11 μμ) at θ = 3 33 arcmins scale. Not from known galaxy populations at z < 6 Most possible: First stars (population III stars) at z 11 But: Needs too large star formation efficiency and/or radiation efficiency Due to insufficient stars forming at z = 11. 32
CIB fluctuation from population III stars CIB fluctuation: δf CCC 0. 00 nwm 2 sr 1 (2 55m at 5 ) Matter density fluctuation at 5 arcmins scale: Δ 5 111 Inferred isotropic flux: F CCC δf CCC Δ 5 = 1 nwm 2 sr 1 CIB flux from first stars (population III) F FF = c 44 ε ρ B c 2 1 f hhhh f z eee f hhhh : mass fraction of the universe inside collapsed halos f : the star formation efficiency ε : radiation efficiency To explain the CIB fluctuation by first stars forming: f hhhh 0. 11 0. 000 ε 10 3 f F FF F CCC Difficult to reach with only adiabatic density perturbation from usual inflation. Solution: isocurvature perturbation in the small spatial scale 33
Large vs Small scale density perturbation Δ 5 10% ~10 6 M halos Isocurvature perturbation due to relaxation leptogenesis θ ~ 5 Large scale fluctuation in CIB due to the adiabatic perturbation from inflaton Increasing the density contrast δ B in small scale increase the number of collapse halos f hhhh 34
Isocurvature Perturbation from Relaxation Leptogenesis 35
Isocurvature Perturbation Fluctuation of φ in each patch of the universe during inflation Variation in baryon asymmetry δ(b B ) through leptogenesis Spatial fluctuation of baryon asymmetry after patches reenter V(φ) φ Baryon asymmetry δy B Baryon density δρ B Produce isocurvature perturbation of baryon φφφ φ φφ No contribution to the initial curvature perturbation. 36
Higgs Fluctuation during Inflation In IC-2, the Higgs φ becomes massless in the last N llll e-fold of inflation due to the inflaton couplings. Quantum fluctuation δφ k H I is produced at the scale 22 smaller than the horizon scale l~h 1 at that time When Higgs becomes massless t = 0 Outside the horizon H I Inside the horizon No difference from Minkowski space After N llll e-fold of inflation t = N llll H H I eee N llll H I δφ k H I 22 Inflationary region p = k/a Physical momentum 37
Higgs Fluctuation during Inflation The horizon at N llll before the end of inflation has a scale k S at present. Power spectrum of φ P φ k H I 22 0 2 for k k S otherwise Baryonic isocurvature perturbation for k > k S δ B k δρ B = δy B = δ φ2 k ρ B Y k B φ 2 2 ln1 2 k k S N k llll θ k k S 38
Constraints on Isocurvature Perturbation CMB: 0. 000 MMc 1 k 0. 1 MMc 1 (Limited by Silk damping) Lyman-α: 0. 1 MMc 1 k 11 MMc 1 Allowed N of e-folds of inflation for the Higgs field: N llll < 44. 2 ll k 11 MMc 1 + 2 3 ll Λ I 10 11 GGG + 1 3 ll T RR 10 12 GGG 39
Growth of density perturbation Baryon isocurvature perturbation only growth after decoupling But the induced potential allows dark matter to grows faster. δ B,0 = 0.025, k S = 65 Mpc 1, N last = 46.5 Matter power Spectrum Contribution from relaxation leptogenesis model only appear in the small scale Silk damping does not affect baryonic isocurvature perturbation. 40
Variance of the density contrast Solid lines: Isocurvature perturbations from k S = 65 Mpc 1 Dashed lines: with only adiabatic perturbation Dash-dot line: δ c = 1.686 Halos with 10 6 M collapsed by z = 10. Mass fraction in collapsed halos Solid lines: 10 6 M halos Reach f halo = 0.16 by z = 10 for k S = 65 Mpc 1 Dashed lines: 10 8 M halos unchanged Can explain the CIB fluctuation excess! 41
Summary Our universe seems to be right on the meta-stable region. The quartic coupling of the Higgs potential turns negative giving a shallow potential. Higgs can obtain a large vacuum expectation during inflation. The relaxation of the Higgs VEV happens during reheating. Higgs relaxation provides the out of thermal equilibrium condition and breaks T invariant. Leptogenesis via the Higgs relaxation is possible. Isocurvature perturbation generated by the relaxation leptogenesis might explain the CIB excess. Higgs relaxation is an important epoch in the early universe. Thanks for your listening! 42
Backup Slides 43
Generating the O 6 Operator LY, Pearce, Kusenko Phys. Rev. D92 (2015) Explicit Fermonic Model: Fields: n 3 Dirac spinors ψ 1i (both left and right): SU(2) doublet, hypercharge -1/2. A Dirac spinor ψ 2 (both left and right): SU(2) singlet, hypercharge -1. Higgs field Φ: SU(2) doublet, hypercharge 1/2. Where Y W = Q T 3. Lagrangian: 44
Parameter Space for Higgs Relaxation Leptogenesis Final lepton asymmetry (lepton-number-to-entropy ration), Y. IC-2 with Λ n = M n, Λ I = 5 10 16 GeV (left) and Λ I = 10 15 GeV (right). 45
Parameter Space for Higgs Relaxation Leptogenesis Final lepton asymmetry (lepton-number-to-entropy ration), Y. IC-2 with Λ n = T 46
What is Zodiacal light? Faint and diffuse triangle shape light seen in the night sky that appears along the zodiac. They come from sunlight scattered by space dust in the zodiacal cloud. 47