SEENET-MTP Balkan Workshop BW2018 10 - 14 June 2018, Niš, Serbia

1. Dark Matter with genuine spin-2 fields
Forget Dark Energy, let’s modify Gravity for Dark Matter!
Federico Urban
CEICO
Institute of Physics
Czech Academy of Sciences
Prague
SEENET-MTP Workshop BW2018
Niˇs – Serbia
June 11th, 2018

2. Outline

3. Outline
I What is bigravity? I

4. Outline
I What is bigravity? I
II A new spin-2 field II

5. Outline
I What is bigravity? I
II A new spin-2 field II
III Spin-2 Dark Matter III

6. Outline
I What is bigravity? I
II A new spin-2 field II
III Spin-2 Dark Matter III
IV Pheno: heavy IV

7. Outline
I What is bigravity? I
II A new spin-2 field II
III Spin-2 Dark Matter III
IV Pheno: heavy IV
V Pheno: light V

8. Outline
I What is bigravity? I
II A new spin-2 field II
III Spin-2 Dark Matter III
IV Pheno: heavy IV
V Pheno: light V
Babichev, Marzola, Raidal, Schmidt-May, FU, Veerm¨ae, von
Strauss PRD, JCAP (2017)
Marzola, Raidal, FU PRD (2018)
L´opez Nacir, FU arXiv 18xx.soon; Marzo, Marzola, FU arXiv 18not.so.soon

9. Bimetric theory essentials Hassan and Rosen (2012) x2
S = d4
x |g|m2
g R(g) + |f |m2
f R(f ) − 2m4
|g| V (g, f ; βn)
1. R(g) is GR for the metric gµν, with strength mg
2. R(f ) is GR for the metric fµν, with strength mf ≡ α mg
3. The interaction potential is V (g, f ) and it depends on 5 parameters βn
4. This action contains no ghosts! It took about 100 yrs to get it right
The ghost-free coupling to matter breaks the symmetry:
Sm = d4
x |g| Lm(g, Φ)

10. What’s in this theory?
Expand around proportional backgrounds fµν = c gµν (for technical reasons)
S(2)
= d4
x |¯g| L
(2)
GR(δG) + L
(2)
FP(δM)
LGR is the (linearised) GR for δG
8 LFP is the Fierz-Pauli spin-2 field δM with mFP∼
√
βnMPl
D These are mixtures of the interaction eigenstates with parameter α
δgµν (δGµν − αδMµν) , δfµν δGµν + α−1
δMµν
MATTER
Sm ∼ d4
x (δGµν − αδMµν) Tµν

11. How does δM gravitate?
δG3
δG2
δM δGδM2
δM3
1 0 1 1/α
δG4
δG3
δM δG2
δM2
δGδM3
δM4
1 0 1 1/α 1/α2
i. All δG vertices have the same strength as in GR
ii. There is no decay of δM into any number of δG
iii. δGδM2
is 1: the response to δG is the same as SM matter
iv. δM self-interactions are enhanced compared to GR

12. Phenomenology 1: heavy
※ The massive spin-2 can be produced via freeze-in:
SM
SM
δG
1
MPl
1
MPl
δM
δM
=
SM
SM
δM
α
MPl
1
α MPl
δM
δM
δM decays universally into all SM particles (but not massless gravitons):
Γ(δM → XX) α2
m3
FP/M2
Pl
The froze-in DM should have the right abundance and not decay too fast:
this can be arranged (see next slide).

13. Heavier and darker
1 2 3 4 5 6 7
20
18
16
14
12
10
8
Log10mFP GeV
Log10Α
Decay
Perturbativity
Production
1 TeV mFP 66.6 TeV 10−12
α 10−16
This range can be extended up to the α 1 region with multiple spin-2 fields Gonz´alez
Albornoz, Schmidt-May, von Strauss (2017)

14. Heavier and darker
1 2 3 4 5 6 7
20
18
16
14
12
10
8
Log10mFP GeV
Log10Α
Decay
Perturbativity
Production
1 TeV mFP 66.6 TeV 10−12
α 10−16
This range can be extended up to the α 1 region with multiple spin-2 fields Gonz´alez
Albornoz, Schmidt-May, von Strauss (2017)

15. Heavier and darker
1 2 3 4 5 6 7
20
18
16
14
12
10
8
Log10mFP GeV
Log10Α
Decay
Perturbativity
Production
1 TeV mFP 66.6 TeV 10−12
α 10−16
This range can be extended down to the MeV to GeV region with dark freeze-out via
3-to-2 interactions Chu, Garcia-Cely (2018)

16. Phenomenology 2: light
A. Fuzzy DM is a very (very) light DM field, usually with mFP 1 eV
B. All we need is a potential dominated by the mass term
This is the typical situation for axions and ALP models
C. Late Universe dynamics: ¨Mij + 3H ˙Mij + m2
FPMij = 0
a This means Mij ∼ a(t)−3/2
cos(mFPt)
b This means T00 ∼ a−3
, and the rest is stuff × cos(mFPt)
c This means, averaging over Hubble, Tµ
ν = ( , 0, 0, 0) with = a−3
d This means Dark Matter!
D. The working mass range is roughly 10−23
eV mFP O(0.1)eV

17. Testing this scenario
1. Fifth force experiments: α 10−2
for mFP O(0.1)eV
2. Lab tests: the electric charge oscillates
A. Atomic clocks experiments
B. Atomic spectroscopy
C. Resonant mass detectors
D. But: Ei Ej ± Bi Bj and Ej Bj ± Bi Ej vs E2
− B2
and E · B
3. Secular change in binary systems orbital parameters
I : DM generates an oscillating environment for the binary
I.I : Fi
= Ri
0j0xj
I.I.I : When oscillations and binary resound we have secular variations
I.V : ˙P 10−17
(P/100d)2
F(Ne)
V : In principle detectable with next generation timing data

18. Summary

19. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields

20. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV

21. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV
Heavy I: production is via freeze-in (leaking from a hot thermal bath)

22. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV
Heavy I: production is via freeze-in (leaking from a hot thermal bath)
Heavy II: the peculiar decay signals can pin down (falsify) this model

23. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV
Heavy I: production is via freeze-in (leaking from a hot thermal bath)
Heavy II: the peculiar decay signals can pin down (falsify) this model
Light I: it is a spin-2 ALP and it is generated via misalignment

24. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV
Heavy I: production is via freeze-in (leaking from a hot thermal bath)
Heavy II: the peculiar decay signals can pin down (falsify) this model
Light I: it is a spin-2 ALP and it is generated via misalignment
Light II: there is a wealth of lab experimental tests for this model, plus
a neat method via binary pulsars

25. Summary
Bigravity is a consistent 4d extension of GR with more spin-2 fields
The new spin-2 are ideal DM candidates
α Heavy: 1 TeV mFP 66.6 TeV
β Kind of heavy: 1 MeV mFP 1 GeV
γ Light: 10−23
eV mFP 1 eV
Heavy I: production is via freeze-in (leaking from a hot thermal bath)
Heavy II: the peculiar decay signals can pin down (falsify) this model
Light I: it is a spin-2 ALP and it is generated via misalignment
Light II: there is a wealth of lab experimental tests for this model, plus
a neat method via binary pulsars
Thank You, and. . .
fi Come visit us at CEICO in Prague fi

26. GRAVITY
@ Prague
Summer School
September 10-14, 2018
gravity-prague.fzu.cz
Lecturers:
Geoffrey Compère Infrared Structure of Gravity
Matthias Gaberdiel Higher-Spin Field Theories
Zohar Komargodski Conformal Field Theory
Samaya N. Nissanke Gravitational Waves
Antonio Padilla The Cosmological Constant
Leonardo Senatore Effective Field Theory of Large Scale Structure
Alexander Vilenkin Inflation and the Multiverse
LOC:
Michal Malinský
Joris Raeymaekers
Lorenzo Reverberi
Ippocratis Saltas
Ignacy Sawicki
Martin Schnabl
Constantinos Skordis
Federico Urban
Alexander Vikman
Credit:WernerBenger/ZIB/AEI/CCT-LSUGravity A2_final finalindd.indd 1 02.05.2018 21:00:26