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Home , Axion, Dark energy

: Dark Abundance Relation

Guy Moore, TU Darmstadt

With Vincent Klaer, Leesa Fleury

• Mystery 1:

• Mystery 2: T-symmetry of QCD

• The Axion: a solution to both mysteries?

• Early of the axion

• How to predict the axion mass if it’s the dark matter

Saariselk¨a, 5 April 2018 Slide 1 of 25 Dark Matter: a Cosmic Mystery

Atoms: . Dark : . Strange value, but possible Dark Matter: MYSTERY! NOT SM!

We only know 3 things about dark matter:

• It’s Matter: gravitationally clumps.

• It’s Dark: negligible , interactions too feeble to be detected except by

• It’s Cold: negligible pressure by z = 3000

Saariselk¨a, 5 April 2018 Slide 2 of 25 Another mystery: T-symmetry in QCD

QCD Lagrangian built of Dim-4 gauge-invariant Lorentz scalars: 1 (i)Θ S = d4x F a F µν + ǫ F µν F αβ , (E) 4g2 µν a 64π2 µναβ a a Z µν αβ µ ν αβ gfabc ν α β ǫµναβFa Fa = ∂ Kµ , Kµ = ǫµναβ AaFa + AaAb Ac  3  Second term integrates to integer NI on A-field singularities.

exp(−SE) = exp(−Sstandard) × exp(iΘNI )

Introduces extra, T violating phase into path integral!

G. ’t Hooft, PRL 37, 8(1976); R. Jackiw and C. Rebbi, PRL 37, 172 (1976); Callan Dashen and Gross, Phys Lett 63B, 334 (1976)

Saariselk¨a, 5 April 2018 Slide 3 of 25 Looking for T: EDM

Put neutron in B~ field – lines up with B~ .

N B B

Is there an (EDM) aligned with spin? If so: looks different when movie runs backwards, T viol!

Saariselk¨a, 5 April 2018 Slide 4 of 25 Neutron EDM and Θ

Theory: Neutron electric dipole moment should exist,

−16 dn = −3.8 × 10 e cm × Θ so long as Θ is not zero! Guo et al, arXiv:1502.02295, assumes Θ, modulo 2π, is small

Experiment: Consistent with zero! Baker et al (Grenoble), arXiv:hep-ex/0602020

−26 |dn| < 2.9 × 10 e cm

Either |Θ| < 10−10 by (coincidence? accident?) or there is something deep going on here.

Saariselk¨a, 5 April 2018 Slide 5 of 25 Axion mechanism

Add singlet complex scalar and some extra UV DOF such that

2 2 µ ∗ m ∗ 2 Arg(ϕ) a ˜µν Lϕ = ∂ ϕ ∂µϕ + 2 ϕ ϕ − 2fa + 2 Fµν Fa 8fa 32π   True Θeff =Θ+ θA with θA = Arg(ϕ). QCD gives θA a potential:

2 − F F F˜ T 2 i(Θ+θA) V (θ ) = − ln D(A ψψ¯ )Det(D/ +m)e 4g × e 32π2 eff A Ω µ Z R R ≃ χ(T )(1 − cos[Θ+θA]) , F F˜(x) F F˜(0) χ(T ) = d4x 32π2 32π2 *Z +β

Forces Θ + θA = 0 automatically, dynamically.

Peccei Quinn PRL 38, 1440 (1977); J. E. Kim, PRL 43, 103 (1979); Shifman Vainshtein and Zakharov, NPB 166, 493 (1980)

Saariselk¨a, 5 April 2018 Slide 6 of 25 χ(T ): what we expect

ln( χ )

χ pt Low T : χ-pt works. mumd 2 2 χ ≃ 2 m f (mu+md) π π Hi T : standard α pt pert-thy works(??) ln(T)

Tc

4 Low T : χ(T ≪ Tc) = (76 ± 1 MeV) Cortona et al, arXiv:1511.02867 −8 High T : χ(T ≫ Tc) ∝ T Gross Pisarski Yaffe Rev.Mod.Phys.53,43(1981) but with much larger errors.

Saariselk¨a, 5 April 2018 Slide 7 of 25 Axion in cosmology

Assume first: ϕ starts homogeneous [inflation]

Classical axion field! Starts oscillating around −1 t = πma . Damped:

• Hubble drag • effect of dma/dt

Pressureless: Acts Like Dark Matter!

2 2 2 Osc. frequency = axion mass: ω = ma = χ/fa

Saariselk¨a, 5 April 2018 Slide 8 of 25 Dark matter density?

More dark matter if oscillations start larger or later:

7/8 2 ρdm ∝ fa θA init (approximately)

• Large fa, (small ma): later transition from cosmological constant to matter, more final

• Initial θA init: larger value, larger starting amplitude.

Because θA init unknown, scenario is not predictive.

Saariselk¨a, 5 April 2018 Slide 9 of 25 Initial state of ϕ field? most likely: randomly different in different places!

• Inflation stretches quantum fluctuations to classical 2 2 ones: ∆ϕ ∼ Hinfl.. If NefoldsH >fa , scambles field. −5 If not: need H < 10 fa to avoid excess “isocurvature” fluctuations in axion field

• Gets scrambled after inflation if Universe was ever really 11 hot T >fa ∼ 10 GeV.

Predictive: if axion=dark matter and we solve dynamics, then → predict fa,ma. L. Visinelli and P. Gondolo, PRL 103, 011802 (2014) Bad: nonperturbative. Good: classical field theory!

Saariselk¨a, 5 April 2018 Slide 10 of 25 Needed Ingredients

Predict relation between Dark Matter Density and Axion Mass assuming space-random starting angle. Challenges:

1. χ(T ): needs Lattice Gauge Thy.

2. Axion field dynamics: classical but with large scale 30 hierarchy fa/H ∼ 10 ≫ 1

1. Recent Borsanyi et al 1606.07494 lattice results. Confirmation?? Claim: I can solve 2.

Saariselk¨a, 5 April 2018 Slide 11 of 25 Obvious approach

Classical real-time lattice using Lagrangian

∗ µ λ ∗ 2 L = ∂µϕ ∂ ϕ+ (2−ϕ ϕ) −χ(t)Re ϕ 8

ϕ(t = 0) random, Hubble drag, Count at end.

Fails: scale hierarchy actually relevant!

Saariselk¨a, 5 April 2018 Slide 12 of 25 Axion strings

ϕ is a complex number – plot as a 2D arrow.

Field generically has vortices. 2D–points. 3D–strings.

Saariselk¨a, 5 April 2018 Slide 13 of 25 Domain walls

2D slice of , When the potential tilts:

Saariselk¨a, 5 April 2018 Slide 14 of 25 Layers of String Energy

− ∼H 1 ∗ 2 2 2 r dr Estr = dz dφ rdr ∇φ ∇φ ≃ fa /2r ≃ πℓfa ∼ −1 r2 Z Z Z Z fa 

Zoom Zoom etc. in in

Look at

Series of “sheaths” around string: equal energy in each ×2 scale, 1030 scale range! ln(1030) ≃ 70.

2 30 2 Log-large string tension Tstr = πfa ln(10 ) ≡ πfa κ Not reproduced by numerics (separation/core ∼ 400)

Saariselk¨a, 5 April 2018 Slide 15 of 25 Getting string tension correct !

String dynamics are controlled by:

2 • String tension and inertia: ∝ κπfa FACTOR of κ

2 • String radiation and inter-string interactions: ∝ πfa NO factor of κ

Relative importance of these effects, and string energy, are κ dependent

We really need to get this right!

Saariselk¨a, 5 April 2018 Slide 16 of 25 Effective field theory

Integrate out string-cores out to radius r0: 2 strings with tension T = κπfa with κ ≡ ln(r0fa):

• Strings with tension T ′2 2 LNG = T dσ y (σ)(1 − y˙ (σ)) Z q

2 • Axion fields θA 3 fa µ LGS = d x ∂µθA∂ θA+χ(1−cos θA) Z 2

• String-axion coupling 3 µν LKR = d xAµνJ Z

Saariselk¨a, 5 April 2018 Slide 17 of 25 Does anyone else have this effective theory?

Plan: find another model which also has:

• Strings obeying LNG

• “Axion” fields obeying LGS

• Coupling between them, LKR

It can have extra DOF as long as I take a limit where they get heavy (along with a → 0)

Saariselk¨a, 5 April 2018 Slide 18 of 25 Trick: global strings, local cores

Theory with U(1) × U(1), one global one gauged:

1 L(ϕ ,ϕ ,A ) = (∂ A − ∂ A )2 1 2 µ 4 µ ν ν µ λ + (2ϕ∗ϕ − f 2)2 + (2ϕ∗ϕ − f 2)2 8 1 1 2 2 h 2 i 2 + |(∂µ − iq1eAµ)ϕ1| + |(∂µ − iq2eAµ)ϕ2|

Pick q1 =6 q2, say, q1 = 4, q2 = 3.

iθ1 iθ2 Two rotation symmetries, ϕ1 → e ϕ1, ϕ2 → e ϕ2 q1θ1 + q2θ2 gauged, q2θ1 − q1θ2 global (Axion)

Saariselk¨a, 5 April 2018 Slide 19 of 25 Two scalars, one gauge field String where each scalar winds by 2π: θ 1 2π B-field almost A B compensates

C gradients outside CAB string. 2 2 2 2 0 θ fa = f /(q1 +q2). 0 2π 2 Red = gauge−equivalent

2 2 dF f 2 2 T ≃ 2πf , = 2 2 , κeff = 2(q1 + q2) . dl (q1 + q2)r

Saariselk¨a, 5 April 2018 Slide 20 of 25 Higher tension = higher initial density, longer lasting, hardier loops

Saariselk¨a, 5 April 2018 Slide 21 of 25 Results

Axions produced vary mildly with increasing string tension

Saariselk¨a, 5 April 2018 Slide 22 of 25 Results

• 10× string tension leads so 3× network density but

• only 40% more axions than with axion-only simulation,

• Fewer (78%) axions than θA init-averaged misalignment

• Axionic string networks are very bad at making axions

• Results in less axion production. Must be compensated by ligher axion mass.

Saariselk¨a, 5 April 2018 Slide 23 of 25 Put it all together

2 Axion production: nax(T = T∗) = (13 ± 2)H(T∗)fa

2 8πε Hubble law: H = 2 , 3mpl 2 4 π T g∗ 4ε : ε = , s = , g∗(1GeV) ≃ 73 30 3T 1 GeV 7.6 Susceptibility: χ(T ) ≃ (1.02(35) × 10−11GeV4)  T  ρ Dark matter: = 0.39 eV s

One finds T∗ = 1.54GeV and ma = 26.2 ± 3.4 µeV

Saariselk¨a, 5 April 2018 Slide 24 of 25 Conclusions

• QCD “generically” violates T symmetry

• Axions: natural explanation, why T viol not observed

• Dark matter density calculable if θA starts random

• Tricky network dynamics – new techniques needed

• Prediction: if DM=Axions, then ma = 26.2 ± 3.4 µeV.

We should go and look for axions, ma ∼ 26 µeV!

Saariselk¨a, 5 April 2018 Slide 25 of 25 How to look for axions

Generally axion also couples to ordinary

θ K θ L = ... + A F µν F˜µν + A F µν F˜µν 32π2 QCD QCD 32π2 EM EM

Since θA varies with time,

ν µν K θA µναβ J = ∂µF + ∂µ ǫ ∂αAβ 8π2 ! Kθ˙ J ν = E˙ + ∇× B + A B i i 8π2 i Axion turns B field into time-oscillating current!

Saariselk¨a, 5 April 2018 Slide 26 of 25 MADMAX experiment Redondo et al 1611.05865

Spaced series of dielectrics, bathed in B~ field B−field

Oscillating current along dielectric interface → emission. Dielectric sheet spacing → constructive interference

26 µeV ≃ 6 Ghz ≃ λ = 5cm

Saariselk¨a, 5 April 2018 Slide 27 of 25 What about ?

Trendy Explanation for “coincidences” or “tunings” Why is Cosmological Constant so small? If it were 100 times bigger, matter would fly apart or collapse before life could evolve. plays dice, with all values occur, but only universes with life get observed.

Why does QCD respect T symmetry? If QCDviolated T, something would go wrong with , which would make life impossible. Nature plays dice, only universes where life is possible get observed. Except that life is fine in a world where Θ = 10−2!

Saariselk¨a, 5 April 2018 Slide 28 of 25