Recent Topics in Axion Cosmology -Isocurvature Perturbations and Alignment
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Recent topics in axion cosmology -isocurvature perturbations and alignment- 30th June 2016 seminar@Osaka U. Fuminobu Takahashi (Tohoku) Kawasaki, FT, Yamada, 1511.05030 Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552 The Strong CP Problem g2 = ✓ s Gaµ⌫ G˜a L✓ 32⇡2 µ⌫ Experimental bound from neutron electric dipole moment reads 10 ✓ < 10− | | Why is ✓ so small is the strong CP problem. cf. More precisely, the physical strong CP phase is ✓¯ ✓ arg det (M M ) ⌘ − u d which makes the problem even more puzzling. A plausible solution is the Peccei-Quinn mechanism where the CP phase is promoted to a dynamical variable: Peccei, Quinn `77, Weinberg `78, Wilczek `78 a g2 = ✓ + s Gaµ⌫ G˜a L✓ f 32⇡2 µ⌫ ✓ a ◆ T Λ QCD T ΛQCD a The QCD axion dynamically cancels the stronga CP phase. Accordingly, the axion DM is produced as coherent oscillations [misalignment mechanism]. f 1.19 ⇤ ⌦ h2 =0.18 ✓2 a QCD a i 1012 GeV 400 MeV ✓ ◆ ✓ ◆ If the axion exists during inflation, it acquires isocurvature fluctuations. δ⌦ ✓ a =2 i ⌦a ✓i δa = Hinf /2π T Λ QCD T Λ QCD a a Axion isocurvature perturbations Adiabatic perturbation Isocurvature perturbation ρ ρ photon photon DM/baryon DM/baryon x x ⌦ δ⌦ ⌦ 2✓ ⌦ H S = a a = a i = a inf ⌦CDM ⌦a ⌦CDM ✓i ⌦CDM ⇡✓ifa S Planck 2015 βiso = P < 0.038 (95% CL) (Planck TT, TE, EE + lowP) + S PR P CMB angular power spectrum Adiabatic Isocurvature Planck CMB angular power spectrum Adiabatic Isocurvature ⌦ ✓ ⌦ H S =2 a i = a inf ⌦CDM ✓i ⌦CDM ⇡✓ifa (Taken from Kawasaki’s slide) Isocurvature constraint on Hinf r = 0.01 9 10 r = 0.1 108 r = ⌦a/⌦DM 107 r = 1 106 7 8 105 Hinf 10 − GeV 104 GeV / 103 inf 102 Anharmonic H 101 effects 100 - 10 1 - 10 2 - 10 3 109 1010 1011 1012 1013 1014 Kobayashi, Kurematsu, FT, 1304.0922 fa / GeV Axion DM is in severe tension w/ many inflation models! Solutions to isocuvature problem 1)Restoration of Peccei-Quinn symmetry during inflation. Linde and Lyth `90 Lyth and Stewart `92 Figure taken from M. Kawasaki’s slide Solutions to isocuvature problem 1)Restoration of Peccei-Quinn symmetry during inflation. Linde and Lyth `90 Lyth and Stewart `92 • Axions are produced from domain walls and 10 axion DM is possible for fa = 10 GeV. Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166 Solutions to isocuvature problem 1)Restoration of Peccei-Quinn symmetry during inflation. Linde and Lyth `90 Lyth and Stewart `92 • Axions are produced from domain walls and 10 axion DM is possible for fa = 10 GeV. Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166 2)(Super-)Planckian saxion field value during inflation. (Saxion could be the inflaton) Linde and Lyth `90 Linde, `91 Axion: phase component Saxion: radial component Solutions to isocuvature problem 3)Resonant mixing with another axion. Kitajima, FT 1411.2011 cf. Hill, Ross `88 2 2 4)Heavy axions during inflation ma & Hinf • Stronger QCD during inflation cf. Dvali, `95, Jeong, FT 1304.8131 Choi et al, 1505.00306 • Extra explicit PQ breaking Dine, Anisimov hep-ph/0405256 Higaki, Jeong, FT, 1403.4186, Barr and J.E.Kim, 1407.4311 FT and Yamada 1507.06387 a The extra PQ breaking term must be sufficiently suppressed at present. Solutions to isocuvature problem In the following, I will talk about two solutions and their implications: (1) The Witten effect Explicit PQ breaking (2) Alignment mechanism Restoration of PQ symmetry Witten effect Witten `79 Let us first consider the θ-term of hidden U(1): This θ is not the ✓e2 ✓e2 strong CP phase. = F F˜µ⌫ = E B L✓ 32⇡2 µ⌫ −8⇡2 · which usually has no effect as it is a total derivative. The term, however, has an interesting effect in the monopole background. B B +θ-term Mono Dyon E pole QM =4⇡/e QM =4⇡/e Q =0 E 6 Witten effect Witten `79 Consider a static EM field and a monopole sitting at the origin: due to Coleman Q rˆ E = gradφ = A0 B = A + M − r r⇥ 4⇡ r2 Then, the Lagrangian is Monopole ✓e2 L = d3r E B ✓ −8⇡2 · Z ✓ ◆ ✓e2 Q rˆ = d3r A0 A + M −8⇡2 r · r⇥ 4⇡ r2 Z ✓ ◆ ✓ ◆ ✓e2Q rˆ = d3rA0 M − 8⇡2 r 4⇡r2 Z ✓ ◆ ✓ ◆ ✓e2Q = d3rA0 M δ(3)(r) − 8⇡2 Z ✓ Electric◆ charge at the origin Witten effect Witten `79 A monopole acquires an electric charge, B and becomes a dyon if ✓ =0 . 6 Dyon E e✓ Q = ne + n =0, 1, 2, E 2⇡ ± ± ··· A monopole magnetic charge Q M =4 ⇡ /e is used. QM =4⇡/e Q =0 E 6 The mass of dyons is heavier than the monopole mass: 1 m2 ✓ 2 M = M + W n D M 2 M − 2⇡ M ✓ ◆ v Q2 + Q2 ' M E The non-zero value ofq θ costs more energy as it induces an electric field around the monopole. Axion coupled to hidden monopoles Kawasaki, FT, Yamada, 1511.05030 Consider the axion coupling to U(1)H: 2 2 e a ˜µ⌫ e a ✓ = 2 Fµ⌫ F = 2 E B L 32⇡ fa −8⇡ fa · Then, the QCD axion acquires an extra mass about a =0 by the Witten effect in the presence of hidden monopoles: 2 ↵ nM ma,M 2 2 ' 16⇡ rcfa cf. Fischler and Preskill, `83 e2 nM :(anti-)monopole number density ↵ = 4⇡ 1 1 rc = : monopole radius ' ev mW •The extra axion mass naturally decreases as the monopole density is diluted by the cosmic expansion. Consistent w/ the neutron EDM constraint. Evolution of axion •The axion starts to oscillate when m 2 H 2. a,M ' 2 ⌦ h2 f − T 65 GeV↵2 M a . osc,1 ' 0.12 1012 GeV ✓ ◆✓ ◆ Witten effect a •No extra axion coherent oscillations are induced during the QCD phase transition if m /H (10) . a,M & O ⌦ h2 0.55 f 1012 GeV↵1.1 M . a . 0.12 ✓ ◆ “Adiabatic suppression mechanism” Linde `96. +QCD instanton Witten effect a Axion abundance Kawasaki, FT, Yamada, 1511.05030 The final axion abundance is given by 3 2 4 2 2 0.12 fa ⌦ h 3 10− ↵− ✓ a ' ⇥ i ⌦ h2 1012 GeV ✓ M ◆✓ ◆ The axion abundance is suppressed, and it is inversely proportional to the monopole abundance! The Witten effect also solves the axion domain wall problem when the PQ symmetry spontaneously broken after inflation. QCD axion and monopole DM 0.12 Monopole dominated DM 2 3 2 12 3 0.10 θinifa /α =(4×10 GeV) 0.08 Ω a h 2 + 2 Ω m 2h h ⌦M h 0.06 2 m = 0.12 Ω 0.04 2 3 2 12 3 θinifa /α =(2×10 GeV) Axion dominated 0.02 2 3 2 12 3 θinifa /α =(1×10 GeV) DM 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 2 ⌦ h 2 Kawasaki, FT, Yamada, 1511.05030 Ωaah Hidden monopole DM The monopoles with mass M =(1 10) PeV account for M − the observed DM. Murayama, Shu 0905.1720 In the minimal case of the ’t Hooft-Polyakov monopole w/o other charged particles, the massive gauge bosons give a larger contribution. Baek, Ko, Park 1311.1035, Khoze, Ro 1406.2291 e.g. The observed DM is realized with v 102 TeV, ↵ = (0.1) ' O for which the monopole fraction is O(10)%. N.B. The massive gauge boson abundance can be reduced by adding matter fields. Discussion • The monopoles (as well as W’) have self-interactions which may solve the small-scale tension of CDM. Baek, Ko, Park 1311.1035, Khoze, Ro 1406.2291 • The monopole DM may also have the SM electromagnetic mini-charges via the kinetic mixing: φa µ⌫ (EM) v µ⌫ (EM) Fa Fµ⌫ F3 Fµ⌫ φa =(0, 0,v) M ⊃ M h i 2 13 For v 10 TeV,M Mp the kinetic mixing is 10− ⇠ ⇠ (& magnetic) ⇠ and it is consistent with observations. cf. Jaeckel and Ringwald, 1002.0329 • If U(1)H is broken by another Higgs, monopoles and W’ become unstable and decay into the SM particles via the portal to the SM Higgs. The QCD axion abundance can be suppressed for even larger f a . Kawasaki, FT, Yamada, 1511.05030 cf. Nomura, Rajendran, Sanches, 1511.06347 Aligned QCD axion Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552 No axion isocurvature perturbations if the PQ symmetry is restored during or after inflation. Is high TR or Hinf necessary? Classical axion window: TR,Hinf & Fa 9 12 10 GeV . Fa . 10 GeV Decay constant = PQ breaking scale? In a simple set-up, V (Φ) Φ F h i⇠ a Φ : PQ scalar However, this is not necessarily the case. If there are multiple PQ scalars, Φ F h i⌧ a is possible. Alignment mechanism The decay constant can be enhanced by the largest hierarchy among the PQ charges in the alignment mechanism, See also Sikivie `86 Kim, Nilles, Peloso, hep-ph/0409138 Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827. Clockwork axion model with N=2: 2 Φ2 Φ V = ( m2 Φ 2 + λ Φ 4) 1 − i | i| i| i| i=1 X 3 + ✏ Φ1Φ2 +h.c. fi + si iai/fi Φi = e p2 2 2 2 3f1a1 f2a2 fa = 3 f1 + f2 ,a= − fa q Alignment with multiple axions Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827.