gravitational wave signals of early universe axion...
TRANSCRIPT
Gravitational wave signals of early universeaxion dynamics
Francesc Ferrer, Washington University in St. LouisB [email protected]
HKUST - IAS. Hong Kong, January 9, 2020.
OVERVIEW AND MOTIVATION
1 48
2 48
UNEXPECTED/SURPRISING?
Most astrophysical models predict M & 20M. But, largerBHs can result from metal-free stars.
Mapelli, 1809.09130
The LIGO/Virgo horizon is z ∼ 0.1− 0.2, but third-generationground-based GW detectors (e.g. Einstein Telescope) will beable to observe mergers up to z ∼ 10.3 48
COULD THEY BE PRIMORDIAL?
Rare Hubble scale perturbations can collapse into BHs:
β ≈ erfc(
δc√2σ
)B.J. Carr & S.W. Hawking, MNRAS 1974; S. Bird et al, 1603.00464; S. Clesse & J.
García-Bellido, 1603.05234; M. Sasaki et al. 1603.08338
4 48
CONSTRAINTS
HSC
EROS
OGLE
Kepler
Femtolensing
NS
WD
Accretion (CMB)
Accretion (X-ray-II)
Accretion (X-ray)
Accretion (Radio)
DF
UFDs
Eri-II
Millilensing
WB
Caustic
Accretion disk (CMB)
Accretion disk (CMB-II)
Sasaki et al. CQG 35 (2018) 063001
5 48
PBHS ARE NOT EXACTLY CDM
101 102
r [pc]
1.0
0.8
0.6
0.4
0.2
0.0δρ
s/ρ
s
fDM = 0. 01 mBH = 10 M¯
fDM = 0. 01 mBH = 30 M¯
fDM = 0. 01 mBH = 50 M¯
fDM = 0. 1 mBH = 30 M¯
fDM = 0. 001 mBH = 30 M¯
T.D. Brandt, ApJ 2016; Koushiappas & Loeb, 1704.01668
6 48
ANOTHER (MORE MASSIVE) PUZZLE
SMBHs reaching & 1010M are present in the centers of mostmassive galaxies, even at large redshifts.
7 48
OUTLINE
1 Overview and motivation
2 Could LIGO detect axions?PBHs from QCD axion dynamics
FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019
GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891, JCAP 2019
3 Conclusions
8 48
COULD LIGO DETECT AXIONS?
OUTLINE
1 Overview and motivation
2 Could LIGO detect axions?PBHs from QCD axion dynamics
FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019
GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891, JCAP 2019
3 Conclusions
9 48
ALTERNATIVE MECHANISMS TO INFLATION?
Phase transitions in the early universe provide a potential avenue:Several violent phenomena naturally occur that can assist ingenerating large overdensities that gravitationally collapse intoBHs: bubble collisions, topological defects, . . .
We will consider axionic string-wall networks.PQ symmetry is broken after inflation: the axion takes differentvalues in different regions and the network is formed when theaxion gets its mass, around the QCD phase transition.
F.F., E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019
Eventually, the network has to decay. Otherwise, the energy density would be quickly
dominated by domain walls.
10 48
RELATION TO BHS
The collapse of closed domain walls, which belong to the hybridstring-wall network can lead to the formation of PBHs.
T. Vachaspati, 1706.03868
It is crucial that the annihilation of the network proceeds slowly.
This mechanism does not rely on (nor complicate) the physicsof inflation.GW astronomy can potentially probe the physics of axions.
11 48
NDW = 1
Only one domain wall is attached to each string. Such topologicalconfigurations quickly annihilate leaving behind a population ofbarely relativistic axions.
T. Hiramatsu, et al., PRD 85, 105020 (2012)
12 48
NDW > 1
There are NDW domain walls attached to every string, each onepulling in a different direction. The network can actually be stable,and dominate the universe.
T. Hiramatsu, et al., JCAP 1301 (2013) 001
13 48
DW PROBLEM?
Lift the degeneracy of axionic vacua by introducing a bias term(dark QCD?). The energy difference between the different minimaacts as a pressure force on the corresponding domain walls.
ΔV
-π πa/η
V(a/η)
14 48
COLLAPSE OF CLOSED DOMAIN WALLS
Once the Hubble length becomes comparable to the closed wallsize R∗, the DW rapidly shrinks because of its own tension.
This occurs at T∗, defined by:
R∗ ∼ H−1 ≈ geff(T∗)−1/2Mp/T 2∗ .
The total collapsing mass has two contributions:
M∗ = 4πσR2∗ +
43π∆ρR3
∗ ≈ 4πσH−2∗ +
43π∆ρH−3
∗
If NDW > 1, then ∆ρ > 0.
15 48
SCHWARZSCHILD RADIUS OF THE DW
The ratio of the Schwarzschild radius of the collapsing DW to itsinitial size R∗ is an important parameter:
p ≡ RS/R∗ ∼2GNM∗
H−1∗
∼ σH−1∗
M2p
+∆ρH−2
∗3M2
p.
If p is close to 1 the DW rapidly enters RS and forms a BH.Otherwise the wall has to contract significantly making it unlikely toform a BH. This is the figure of merit for PBH formation.
(Deviations from spherical symmetry, radiation friction during collapse can partly modify
this picture.)
16 48
17 48
18 48
19 48
20 48
21 48
22 48
23 48
TEMPERATURE DEPENDENCE
Two regimes:When the tension dominates, M∗ ∼ T−4
∗ an p ∼ T−2.When the energy density dominates, M∗ ∼ T−6
∗ an p ∼ T−4.The duration of the hybrid network has a huge impact: as thetemperature decreases it becomes more likely to form a blackhole, and heavier black holes result from DWs which collapse later.
Long-lived string-wall networks are essential. This requiresmultiple DWs attached to each string.
24 48
LONG LIVED AXIONIC STRING-WALL NETWORKS
As soon as the axion obtains its potential from nonperturbativeQCD effects domain walls become relevant. This occurs at atemperature
3H(T1) = m(T1)⇒ T1 ∼ GeV.
At around the same time, the homogeneous component of theaxion field starts to oscillate and generates CDM. If NDW > 1, thenetwork is stable, but a bias term can be added to avoid the DWproblem:
VB(a) = A4B
[1− cos
(av
+ δ)].
There is now an energy difference ∆ρ ≈ A4B, which balances the
tension untilσ ≈ A4
BH−1 ⇒ T2 ∼√
MP∆ρσ
25 48
NDW > 1 NETWORKS
Crucial points:There can be a significant separation between T1 and T2.Closed structures surrounding regions with energy A4
B canexist.
The addition of the bias term misaligns the axion:
θmin ≈A4
BNDW sin δ
m2NDWF 2 +A4B cos δ
. 10−10.
The phase is related to T2 through AB . At constant δ, this corresponds to a line in the
log F − log T2 plane. We would like δ ∼ 1.
26 48
SN 1987A
Chang et al. ' 18 PDG ' 18
p = 10-8
p = 10-6
p = 10-4
δ = 0.1
δ = 1
10-8 M⊙
10-4 M⊙
1M⊙
Ωa >ΩCDM
107 108 109 1010 101110-4
10-3
10-2
10-1
100
101
F[GeV]
T2[GeV
]
27 48
AXION-QCD VS ALPS
For the QCD axion we find an interesting region around
fa ∼ 109 GeV.
PBHs of mass 10−4M can form with p ∼ 10−6.For generic ALPs we can reach larger probabilities p ∼ 10−3
in scenarios whereT2 ∼ keV.
Interestingly much larger BHs, . 108M could be formed.
28 48
LATE COLLAPSES
Most of the axionic string-wall network disappears at T2, which iswhen the vacuum contribution starts dominating, and both p andM∗ increase steeply.But, 1− 10% of the walls survive until ∼ 0.1T2, when:
p ∼ 1M∗ ∼ 106M
Hence, a fraction f ∼ 10−6 of the DM end up forming SMBHs!Also influence LSS.
B. Carr & J. Silk, 1801.00672
29 48
LATE COLLAPSES
SN 1987 A
Ωa>ΩCDM
PDG ' 18
T2 ≃ 7MeV
p = 0.01
p = 0.1
p = 1
104 M⊙
106 M⊙
108 M⊙
2×108 4×108 6×108 8×10810-4
10-3
10-2
F[GeV]
T*[GeV
]
30 48
ORIGIN OF THE BIAS TERM
Planck suppressed operators are unlikely.A dark gauge sector with ΛB ∼ MeV is an interestingpossibility.
A. Caputo & M. Reig, 1905.13116
31 48
OUTLINE
1 Overview and motivation
2 Could LIGO detect axions?PBHs from QCD axion dynamics
FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019
GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891, JCAP 2019
3 Conclusions
32 48
ALPS
We will now consider generic pNGB resulting from a U(1)symmetry spontaneously broken at a scale fa ( vew).
Couplings to SM particles are suppressed by inverse powers of fa.
Φ(x) =1√2
[fa + φ(x)] eia(x)/fa
mass ∼ fa very light
For low-energy phenomenology, φ is integrated out and ignored.We will look at the dynamics of φ around the fa scale and find thatit can provide additional constraints on the ALP model.
33 48
MODEL
Consider a non-zero coupling
ALP Higgs
Then, the phase transition at the scale fa could be stronglyfirst-order and produce a stochastic GWs.
V0 = −µ2|H|2 + λ|H|4 + κ|Φ|2|H|2 + λa
(|Φ|2 − 1
2f 2a
)2
.
In terms of the real scalar field components,
V0(φ,h) =λa
4
(φ2 − f 2
a
)2+κ
4φ2h2 − µ2
2h2 +
λ
4h4
34 48
FIRST ORDER PHASE TRANSITION
A FOPT along the φ direction while maintaining the VEV of hequal to zero, can occur if:
µ2 ≤ 2λλa
κf 2a
We will choose µ that saturates the identity and ignore thedependence of the effective potential on h.
The radiative contribution of the scalar to the Higgs mass has tobe cancelled out in a UV complete escenario (e.g. by vector-likefermions at the µ-scale).
For related ideas & extensions, see also
Delle Rose, Panico, Redi & Tesi 1912.06139
von Harling, Pomarol, Pujolas & Rompineve 1912.07587
35 48
FIRST ORDER PHASE TRANSITION
Fixing fa, scan the region (κ, λa) to find where a FOPT can takeplace.
36 48
GRAVITATIONAL WAVE PRODUCTION
h2ΩGW ' h2Ωφ + h2ΩSW + h2ΩMHD
C. Caprini et al. 1910.13125
Input quantities to be calculated from our model parameters:Ratio α of vacuum energy density released in the PT toradiation.Rate of the PT, β/H∗.Latent heat fractions for each of the three processes.Bubble wall velocity.
In the phenomenologically relevant cases, the bubble wall collisionand sound wave contributions dominate.
37 48
Tc & Tn
Consider 103 GeV ≤ fa ≤ 108 GeV.
38 48
β & α
A sizeable GW signal can be generated for large α and small β.When κ ≈ 1 & λa ≈ 10−3 it reaches h2ΩGW ≈ 10−12.
39 48
DETECTION PROSPECTS
40 48
DETECTION PROSPECTS
41 48
DETECTION PROSPECTS
42 48
DETECTION PROSPECTS
43 48
COMPARISON WITH OTHER ALP CONSTRAINTS
10-8 10-5 0.01 10 104 107
10-12
10-10
10-8
10-6
ma [eV]
gaγ
γ[GeV
-1]
LSW
helioscopes
Sun
HB stars
γ-rays
haloscopes
DFSZ
KSVZ
telescopes
xion
X-rays
EBL
CMB
BBN
SN
beamdum
p
TianQin
BBO
CE
44 48
COMPARISON WITH OTHER ALP CONSTRAINTS
10-8 10-5 0.01 10 104 107
10-12
10-10
10-8
10-6
ma [eV]
gaγ
γ[GeV
-1]
ALPS II
STAX
ALPSIII
telescopes
helioscopes
DFSZ
KSVZ
SHiP
TianQin
BBO
CE
45 48
COMPARISON WITH OTHER ALP CONSTRAINTS
10-4 0.01 1 100 104 106 108
10-13
10-11
10-9
10-7
ma [eV]
gaee
DSFZ
KSVZ
Edelweiss
Red Giants
E137
MINOS/MINERvA
TianQin
BBO
CE
46 48
COMPARISON WITH OTHER ALP CONSTRAINTS
10-6 0.001 1 1000 106 109
10-9
10-7
10-5
10-3
ma [eV]
gaNN
DFSZ KSVZ
SN1987A
Cavendish
magnetometer
BBO
TianQin
CE
47 48
CONCLUSIONS
CONCLUSIONS
The observed LIGO BHs masses & 20M are unexpectedlylarge to result from stellar evolution considerations, and couldbe hinting at PBHs.Axionic topological defects with NDW > 1 lead to a newNetwork Annihilation epoch that can potentially generatePBHs of up to 106M, and that can be tested by LISA.A FOPT at the PQ scale could take place in some ALPmodels. The GW signal strength could be as large ash2ΩGW ∼ 10−12, within reach of next generation GWobservatories.
48 / 48