Gravitational wave signals of early universe axion...

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

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





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.

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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.

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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)

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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)

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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

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

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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.

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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

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OUTLINE





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.

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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.

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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.

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Tc & Tn

Consider 103 GeV ≤ fa ≤ 108 GeV.

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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.

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DETECTION PROSPECTS

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DETECTION PROSPECTS

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DETECTION PROSPECTS

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DETECTION PROSPECTS

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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

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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

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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

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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.

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Gravitational wave signals of early universe axion...

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