International Symposium on “Revealing the history of the universe with underground particle and nuclear research 2019” @Tohoku University, March 7-9, 2019 Axion Cosmology Masahiro Kawasaki (ICRR & Kavli IPMU, The University of Tokyo)
1. Axion • Axion is predicted in PQ mechanism which solves strong CP problem in QCD • Axion is the Nambu-Goldstone boson associate with U(1) PQ breaking and can be identified with the phase of PQ scalar Φ = | Φ | e i θ = ( η + ϕ ) e ia/ η η : breaking scale • Axion acquires mass through QCD non-perturbative e ff ect F a = η /N DW � − 1 � F a m a � 0 . 6 � 10 − 5 eV 10 12 GeV N DW : domain wall number • Axion is a good candidate for dark matter of the universe 2
1. Axion • Cosmological evolution of axion (PQ scalar) PQ symmetry breaking after inflation scenario A Formation of topological defects Domain wall problem scenario B PQ symmetry breaking before inflation Isocurvature perturbation Isocurvature perturbations problem 3
Today’s Talk • Introduction • PQ symmetry breaking after inflation scenario A Cosmological evolution of axion Comic axion density Non-topological objects of axions • PQ symmetry breaking before inflation scenario B Isocurvature perturbation problem Suppression of Isocurvature Perturbations • Conclusion 4
2. Cosmological Evolution of Axion (PQ after inflation) V ( Φ ) scenario A T � η • U PQ (1) symmetry is broken T � F a Axion is a phase direction of PQ scalar and massless Φ = | Φ | e i θ = | Φ | e ia/ η m a = 0 Formation of Cosmic Strings T = 0 T � Λ QCD N DW =2 V ( a ) • Axion acquires mass through non-perturbative e ff ect U PQ (1) is broken to Z N DW π 2 π 0 Coherent oscillation θ = a / (F a N DW ) Formation of Domain Walls 5
• Domain walls attach to strings N DW ≥ 2 N DW =1 N DW =3 wall string Collapse Virenkin Everett (1982) Stable and dominate the universe Barr Choi Kim (1986) Domain Wall Problem Axion overproduction 6
3. Cosmic Axion Density 3.1 Coherent axion oscillation V ( a ) N DW = 1 H � m a ( T ∗ ) • 0 2 π F a a Axion field starts to oscillate at T = T ∗ • Coherent oscillation of axion field gives a significant contribution to the cosmic density ( ) Ω CDM h 2 � 0 . 12 � 1 . 19 spatial average � F a Ω a, osc h 2 � 7 � 10 − 4 � θ 2 ∗ � 10 10 GeV � θ 2 ∗ � � 6 θ ∗ = a ∗ /F a : misalighnment angle at T ∗ including anharmonic e ff ect F a ' 2 ⇥ 10 11 GeV Ω a, osc h 2 ' 0 . 12 if 7
3.2 Axions from strings • Axionic strings are produced when U(1) PQ symmetry is spontaneously broken 2 • Numerical Lattice Simulation scaling parameter ξ 1.5 Hiramatsu, MK, Sekiguchi, Yamaguchi, Yokoyama (2010) MK, Saikawa, Sekiguchi (2014) • 1 String network obeys scaling solution 0.5 ρ string = ξ µ ( µ ∼ η 2 : string tension ) 0 t 2 5 10 15 20 25 proper time t/t crit ξ = 1 . 0 ± 0 . 5 • Scaling solution is established by emitting axions • Emitted axion energy ρ a, str is estimated from ρ string • If we know average energy we can estimate the present ¯ ω a axion density as ρ a = m a ( ρ a, str / ¯ ω a ) 8
Density of Axions from Strings • Energy Spectrum MK, Saikawa, Sekiguchi (2014) differential spectrum Δ P free (k;12.25t crit ,25t crit ) ( horizon scale ) − 1 ∼ 5 10 3 peak at low k ~ (horizon scale) -1 ~1/t 10 2 suppressed at higher k 10 1 • Average energy parameter 10 0 � a = � 2 � ¯ 10 -1 t ✏ = 4 . 02 ± 0 . 70 10 -2 0 50 100 150 200 MK, Saikawa, Sekiguchi (2014) comoving wavenumber k • Cosmic density of produced axion ◆ 1 . 19 ✓ F a Ω a, string h 2 = (7 . 3 ± 3 . 9) × 10 − 3 N 2 DW 10 10 GeV � 1 . 19 � F a Ω a, osc h 2 � 4 � 10 − 3 10 10 GeV 9
3.3 Axion from Domain Walls (N DW =1) • Axion energy density from collapsing domain walls can be estimated in the same way as strings • Simulation of string-wall network Lattice simulation with N(grid) = (512) 3 Hiramatsu, MK, Saikawa, Sekiguchi (2012) Scaling property κ = 0.40 1.4 κ = 0.35 κ = Λ QCD /F a κ = 0.30 Average energy 1.2 κ = 0.25 κ = 0.20 area parameter A 1 • Axions from collapsed domain walls 0.8 0.6 Ω a, wall h 2 =(5 . 4 ± 2 . 1) × 10 − 3 0.4 0.2 ◆ 1 . 19 ✓ F a 0 0 2 4 6 8 10 12 × conformal time τ / τ c 10 10 GeV 10
Cosmic Axion Density (N DW =1) • Total cosmic axion density Ω a, tot h 2 = Ω a, osc h 2 + Ω a, string h 2 + Ω a, wall h 2 ◆ 1 . 19 ✓ F a = (1 . 7 ± 0 . 4) × 10 − 2 10 10 GeV Ω CDM h 2 � 0 . 12 • Constraint on F a F a . (4 . 2 − 6 . 5) × 10 10 GeV m a & (0 . 9 − 1 . 4) × 10 − 4 eV 11
• MK, Saikawa, Sekiguchi (2014) 3.4 Axion from Walls (N DW ≥ 2) Ringwald, Saikawa (2015) • Wall-string networks are stable and soon dominate the universe Domain Wall Problem • The problem can be avoided by introducing a “bias” term which explicitly breaks PQ symmetry 3 Φ e − i δ + h . c . V bias = − Ξ η 3 � w bias � w/o bias Sikivie (1982) Ξ : bias parameter 2 δ : phase of bias term V • Bias term lifts degenerated vacua 1 and leads to DW annihilation 0 large bias is favored 0 π −π −π/2 π/2 θ a = a/f a • Bias term shifts the minimum of the potential and spoils h θ i 6 = 0 the original idea of Peccei and Quinn small bias is favored More stringent constraint on F a Axion can be dark matter for smaller F a 12
3.5 Summary: case of symmetry breaking after inflation 10 8 10 9 10 10 10 11 10 12 MK, Saikawa, 10 -2 10 -3 10 -4 10 -5 Sekiguchi (2014) parameter ranges where axion can be dark matter • Axion can be dark matter of the universe for F a ~ 10 9 GeV or ~5X10 10 GeV and can be probed by the next generation experiments 13
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