宇宙の進化と素粒子模型
宇宙線研理論グループ
川崎雅裕
東大宇宙線研 ：川崎、久野、浅野、 平松 、他
東大数物：高橋京都大学：瀬波
金沢大：青木東北大：浅野、郡
富山大：松本、兼村
青山学院大：山口
神奈川大：粕谷
佐賀大：高橋国内旅費：２0万円

2010年12月17日金曜日

Axionic Strings and Domain Walls
東大宇宙線研 ：関口、川崎、齊川
東大ビッグバン：横山
東工大：山口京大基研：平松

2010年12月17日金曜日

1.1 Axion• QCD Strong CP Problem
QCD

g2aµν a
L = Lθ=0 + θ
FF̃µν
232π

Experimentθ � 10Why is θ so small?

strong CP problem

Peccei-Quinn Mechanism

Peccei, Quinn (1977)• Solution of Strong CP Problem
U(1) PQ

U(1) PQ at Fa : PQ scale

Nambu-Goldstone boson• Axion is a candidate for Dark Matter2010年12月17日金曜日−10AXIONCP

2.2 Cosmological Evolution of Axion••PQ scalar ΦaT � Fa

V (Φa ) T � Fasymmetry breaking of U (1)PQ

Φa = |Φa |eiθa= |Φa |eia/Faaxion is a phase direction of PQ scalarma = 0Axionic String

T =0

mass through QCD instanton effect• T ∼ ΛQCD axion acquires
��ma ∼ 10−5eVFa
1012 GeV−1V (a)

Domain Wall• H � maaxion oscillation0significant contribution to cosmic density

2010年12月17日金曜日

2πFaa

3 Axionic String• Global strings are produced when U(1) PQ symmetry isspontaneously broken• After production string network obeys scaling solution
O(1) strings in a horizon volumeµρstring = ξ 2t(µ : string tension)• Strings lose their energy by emitting axions
Energy spectrum of axions?
Controversy�

P (k) ∼khorizon(Devis, Shellard)

1/k(Sikivie)• New Simulation ( Hiramatsu et al 2010 )2010年12月17日金曜日

Simulation
Hiramatsu, MK, Sekiguchi,Yamaguchi,Yokoyama (2010)• Field theoretical simulation
Pseudo Power Spectrum Estimator•(PPSE)
scheme3•New string identification• N(grid) = (512)• At the end of simulation(space resolution) = 1.4 (string width)(simulation box) = 1.6 (horizon)

2010年12月17日金曜日

Simulation
Hiramatsu, MK, Sekiguchi,Yamaguchi,Yokoyama (2010)• Field theoretical simulation
Pseudo Power Spectrum Estimator•(PPSE)
scheme3•New string identification• N(grid) = (512)• At the end of simulation(space resolution) = 1.4 (string width)(simulation box) = 1.6 (horizon)

2010年12月17日金曜日

Simulation
Hiramatsu, MK, Sekiguchi,Yamaguchi,Yokoyama (2010)• Field theoretical simulation
Pseudo Power Spectrum Estimator•(PPSE)
scheme3•New string identification• N(grid) = (512)• At the end of simulation(space resolution) = 1.4 (string width)(simulation box) = 1.6 (horizon)

2010年12月17日金曜日

Simulation

Hiramatsu, MK, Sekiguchi,Yamaguchi,Yokoyama (2010)2

scaling parameter !

ξ = 0.87 ± 0.14
µρstring = ξ 2t

10.5051015proper time t/tcrit2025(horizon scale)−1 ∼ 5

Figure 5: Time evolution of the scaling parameter ξ obtained by averaging over 20 realizations.
[Note 3that data points are not homogeneously placed in t, but in√10τ ∝ t.]•Energy Spectrum
peaked at horizon scale
exponentially suppressedat higher momentum

2010年12月17日金曜日

1.5

differential spectrum !Pfree(k;12.25tcrit,25tcrit)•Scaling solution

4.2

2

10

Net energy spectrum of radiated axions

1
Figure 6 shows the10 energy spectra of radiated axions at t1 = 12.25tcrit (left) and t2 = 25tcrit(right), that are estimated from the 20 realizations used in Section 4.1. The amplitude
2of energy spectrum
0 at t1 is about (t1 /t2 ) # 0.24 times that at t2 . This is because theenergy density 10of free axions scales as R(t)4 , without emission or absorption. We see aclear exponential behavior at large k after the removal of the contamination from strings.
-1
As we see in10Section
4.1, the system of axionic strings are already in the scaling regime.
Most of axions at this epoch are however emitted before the settlement into the regime. Inorder to extract the energy spectrum of axions radiated during the scaling regime, we need-2
to differentiate10
the energy spectra at different times. We define the differential spectrumof radiated axion between t1 and t2 ,

050
100
150
44
∆Pfree (k; t1 , t2 ) ≡ comoving
R(t2 ) Pfree (k,t2 ) − R(t1 ) Pk
free (k, t1 ).
wavenumber

200(25)

If there are no emission nor absorption of axions, the energy density of axion scales as
Therefore, ∆Penergy
is the net energy
spectrumaxions
of axionsradiatedt1fromstrings.crit andfree (k, t) spectrum
FigureR(t)7: 4 . Differentialof radiatedbetween= 12.25t

Constraint on PQ scale• Cosmic density of produced axionΩaxion h = 1.66 ± 0.252

�• Constraint
FPQ ≤ 3 × 1011 GeV

2010年12月17日金曜日

ΛQCD
400MeV��FPQ1012 GeV

�1.19

4. Axion Domain Wall

• QCD scale
U(1)discrete Z NPQ

Domain Wall Formation

N=3•N>1Domain Wall Problem

V

Biased Potential
Domain wall decay2 2λm
η
22 2V (φ) = (|φ| − η ) +(1 − cos N θ) + δV
24N

δV = −ξη (φe32010年12月17日金曜日−iδ+ h.c.)a2D simulation
N=48

N=2

N=4N

FIG. 4: The time evolution of the comoving area density of domain

FIG. 1: Theofdistributionof thepotential
energyandthe PQ
phase of thePQ fieldθ the(right)
the caseNDW =The distribution
the potential
energy(left) andthe(left)
phaseof=the(right)
casewithN
2 (top),
NDW
3 (rightfield
top),θandNDW with= 4 (bottom).
InDW
the =casewith NDW
NDW =4 (middle),
NDW =at6the(bottom)
τsize= 56.
The figures
size of these
set to bequarter
4 (middle),
andNDW = 6and(bottom)
time τ at= the56. time
Theof theseset figures
to be aisquarterof athesize ofof th
the restriction
given by eq.is(15).
2010年12月17日金曜日
the simulation box. In the distribution of the energy density, the white region corresponds to the vacuum (V (φ) ! 0),Constraints• EDMξη 2θ̄ � 2 � 10−11m
before wall
• Decaydomination
ξ > 3 × 10 N
3−3�mMp

�27*956!"#$%&!#'()!"#$%&!#'(*56796

D22&B40E&!"#$!"#$%&!#'(+,-./01234/.%&!#'(),-./01234/.%&!#'(*56799,-./01234/.%&!#'(+567+634=./>2-?.
7+956

56786 856

2010年12月17日金曜日

F#$@?11&A2BC>?DC2>

56:56;

5656

5655565)565<565

FIG. 7: The contours of the various observational constraints in the parameter space of Fa and ξ. Thebound given by eq. (24) and the dot-dashed line shows the bound given by eq. (26), for a domain wa(red), NDW = 4 (green) and NDW = 6 (blue), respectively. The gray region denoted by “too much NED