P mor al Black Hol as Dark Ma er Cleveland 16th of May 2017 P!mor"al Black Hol# as Dark Ma$er Black...
Transcript of P mor al Black Hol as Dark Ma er Cleveland 16th of May 2017 P!mor"al Black Hol# as Dark Ma$er Black...
Florian Kühnel
work in particular with !
Bernard Carr Katherine Freese Marit Sandstad Glenn Starkman
BLV2017 Cleveland 16th of May 2017
Primordial Black Holesas
Dark Matter
Black Holes
©Warner Bros.
Oscar Klein Medal 2016
Awarded to Milestone physicist Kip Thorne
Oscar Klein Medal 2016
Awarded to Milestone physicist Kip Thorne
… more later…
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
To form smaller black holes we need higher density
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
To form smaller black holes we need higher density
Compare to cosmological density
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
To form smaller black holes we need higher density
Formation at early times; primordial black holes (PBHs)
Compare to cosmological density
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
To form smaller black holes we need higher density
Formation at early times; primordial black holes (PBHs)
Compare to cosmological density
Masses of primordial black holes:
Primordial Black Holes —Formation
Black-hole (BH) formation for .
Astrophysical: From down to , but not lower.
Have a look at the density
To form smaller black holes we need higher density
Formation at early times; primordial black holes (PBHs)
Compare to cosmological density
Masses of primordial black holes:
Primordial Black Holes —Evaporation
Quantum Mechanics
General Relativity
Thermodynamics
Black-hole radiation[Hawking 1974]
Primordial Black Holes —Formation
Formation of primordial black holes
http://www.damtp.cam.ac.uk/research/gr/public/cs_top.html
Cosmic string loops
Primordial Black Holes —Formation
Formation of primordial black holes by
http://www.damtp.cam.ac.uk/research/gr/public/cs_phase.html
Cosmic string loops
Primordial Black Holes —Formation
Formation of primordial black holes
Bubble collisions
by
Cosmic string loops
Primordial Black Holes —Formation
Formation of primordial black holes
Pressure reduction
Bubble collisions
0.0 0.5 1.0 1.5 2.0
0.34
0.36
0.38
0.40
0.42
0.44
M/M�11
�c
by
Cosmic string loops
Primordial Black Holes —Formation
Formation of primordial black holes
Pressure reduction
Large density perturbations
Bubble collisions
https://ned.ipac.caltech.edu/level5/Sept12/Kravtsov/Kravtsov3.html
by
Cosmic string loops
Primordial Black Holes —Formation
Formation of primordial black holes
Pressure reduction
Large density perturbations
[Carr 1975]Simple estimate:
Jeans lengthscale of the over density
Bubble collisions
https://ned.ipac.caltech.edu/level5/Sept12/Kravtsov/Kravtsov3.html
by
Given the density distribution
Primordial Black Holes —Formation
black holesprimordial
derive the PBH density parameter:
Given the density distribution
Primordial Black Holes —Formation
black holesprimordial
variance derive the PBH density parameter:
In the Gaußian case
Given the density distribution
Primordial Black Holes —Formation
black holesprimordial
separate universes
variance derive the PBH density parameter:
In the Gaußian case
Given the density distribution
Primordial Black Holes —Formation
black holesprimordial
separate universes
variance derive the PBH density parameter:
In the Gaußian case
If furthermore , we find that the fractionof collapsed universes becomes
Primordial Black Holes —Probes of Scales
Probe a huge range of scales:
Planck relics, Extra dimensions and higher-dimensional black holes, …
Quantum Gravity:
Primordial Black Holes —Probes of Scales
Probe a huge range of scales:
Planck relics, Extra dimensions and higher-dimensional black holes, …
Quantum Gravity:
Early Universe: Baryogenesis, Nucleosynthesis, Reionisation, …
Primordial Black Holes —Probes of Scales
Probe a huge range of scales:
Planck relics, Extra dimensions and higher-dimensional black holes, …
Quantum Gravity:
Early Universe: Baryogenesis, Nucleosynthesis, Reionisation, …
High-Energy Physics: Cosmological and galactic gamma-rays, …
Primordial Black Holes —Probes of Scales
Probe a huge range of scales:
Planck relics, Extra dimensions and higher-dimensional black holes, …
Quantum Gravity:
Early Universe: Baryogenesis, Nucleosynthesis, Reionisation, …
High-Energy Physics: Cosmological and galactic gamma-rays, …Critical phenomena, Cold dark matter, Dynamical effects, Lensing effects, Gravitational waves, Large-scale structure, Black holes in galactic nuclei, …
Gravity:
Primordial Black Holes —Some Numbers
Mass range:
Size:
Number in our Galaxy:
Distance:
Consider an example of primordial black holes constituting all of the dark matter:
Primordial Black Holes —Constraints
[Carr et al. 2010]
10-30
10-25
10-20
10-15
10-10
10-5
100
0 10 20 30 40 50
`’
log10(M/g)
Planck
LSP
Entropy
BBN
CMB
Galactic aEGB
21cm
1PBH
GRB
GW
WMAP3FIRAS
MACHOQSO
WBDF
LSS
Primordial Black Holes —Constraints
[Carr et al. 2010]
10-30
10-25
10-20
10-15
10-10
10-5
100
0 10 20 30 40 50
`’
log10(M/g)
Planck
LSP
Entropy
BBN
CMB
Galactic aEGB
21cm
1PBH
GRB
GW
WMAP3FIRAS
MACHOQSO
WBDF
LSS
Primordial Black Holes —Constraints
[Carr et al. 2010]
10-30
10-25
10-20
10-15
10-10
10-5
100
0 10 20 30 40 50
`’
log10(M/g)
Planck
LSP
Entropy
BBN
CMB
Galactic aEGB
21cm
1PBH
GRB
GW
WMAP3FIRAS
MACHOQSO
WBDF
LSS
Note that
and hence
Primordial Black Holes —Observed?
Milestone detection of gravitational waves by LIGO
Confirmation of two merging black holes (GW150914 & holes (GW151226)
Masses for all BHs:
Primordial Black Holes —Observed?
Milestone detection of gravitational waves by LIGO
Confirmation of two merging black holes (GW150914 & holes (GW151226)
Masses for all BHs:
Could be PBHs![Bird et al. 2016]
Critical Collapse
[Miller et al. 2004]
Usually: Assume
Critical scaling:[Choptuik ’93]
horizon mass
density contrast
Radiation domination:
Critical Collapse
10 20 50 1000.001
0.005
0.010
0.050
0.100
0.500
1
M/M�11
f
dark-matter fraction
How would this look for monochromatic mass function?
Critical Collapse — Generic Predictions
ShiftLowering
Example I: Hybrid inflation
10-22 10-17 10-12 10-7 10-20.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
M/M�11
�Eq
( Broadening)more on next side…
Critical Collapse — Phase Transitions
0.001 0.010 0.100 1 10 100
10-7
10-5
0.001
0.100
M/M�11
�Eq
0.0 0.5 1.0 1.5 2.0
0.5
1.0
1.5
2.0
M/M�11
�
0.0 0.5 1.0 1.5 2.0
0.34
0.36
0.38
0.40
0.42
0.44
M/M�11
�c
Example II: Phase transition (pressure reduction)
ShiftLoweringBroadening
Critical Collapse — Phase Transitions
LIGO mass range:
10 20 50 1000.001
0.005
0.010
0.050
M/M�11
�Eq
Running Mass
Axion-Curvaton
Non-Spherical Effects
Non-Sphericity
10-6 10-5 10-4 0.001 0.010 0.100 1
10-7
10-5
0.001
0.100
M/M�11
�Eq� = 1.61; � = 0.5� = 0.65; � = 0.64� = 0.47; � = 0.62Spherical
Simple estimate:
prolatenessellipticity
spherical threshold
ellipsoidal threshold
As the collapse starts along shortest axis first,consider collapse of largest enclosed sphere (green curve):
Non-Gaußian Effects
Non-Gaußian Effects
Remember that PBH production is deep inside the tail of the distribution.
This means, PBH production is largely sensitive to non-Gaußianity (skewness, kurtosis, …).
… even more so, as the PBH abundance depends exponentially on the amplitude of the perturbations.
… typically larger than 5 to 10 sigma
Non-Gaußian Effects
This means, PBH production is largely sensitive to non-Gaußianity (skewness, kurtosis, …).
… even more so, as the PBH abundance depends exponentially on the amplitude of the perturbations.
As shown by Byrnes et al., there is a very strong modal coupling between long- and short-wavelength modes.
… typically larger than 5 to 10 sigma
This generates iso-curvature perturbations, and basically rules out all multi-field models with significant non-Gaußianity.
Remember that PBH production is deep inside the tail of the distribution.
[Byrnes et al. 2014]
[Byrnes et al. 2015]
Non-Gaußian Effects
10 20 50 1000.001
0.005
0.010
0.050
M/M�11
�Eq
Running Mass
Axion-Curvaton
10 20 50 1000.001
0.005
0.010
0.050
M/M�11
f
dark-matter fraction
[See also work by [Byrnes et al.]
Extended Mass Spectra and Constraints
1 5 10 50 100 500 10000.0
0.2
0.4
0.6
0.8
1.0
M/M�11
f
EROS
Eridanus II
WB
1 5 10 50 100 500 10000.0
0.2
0.4
0.6
0.8
1.0
M/M�11
f
EROS
Eridanus II
WB
I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI
Extended Mass Spectra and Constraints
Extended Mass Spectra and Constraints
1 5 10 50 100 500 10000.00
0.01
0.02
0.03
0.04
0.05
0.06
M/M�11
df/dm
I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI
Running Mass
Axion-Curvaton
More Systematic Study
Of course, the best would be to recalculate each constraint with a given mass function.
Use an approximate mass function for approximately generic statements:
Given the spread through critical collapse, this is remarkably close to most of the specific models.
[Green et al. 2016]
Eg., less than 10% difference in prediction of microlensing events using this mass function wrt. the ones mentioned in this talk.
More Systematic Study
Of course, the best would be to recalculate each constraint with a given mass function.
Use an approximate mass function for approximately generic statements:
This would need to be done for each case separately.
Given the spread through critical collapse, this is remarkably close to most of the specific models.
[Green et al. 2016]
Eg., less than 10% difference in prediction of microlensing events using this mass function wrt. the ones mentioned in this talk.
More Systematic Study
[Green 2016]
Extended Mass Spectra and Constraints
10-16 10-12 10-8 10-4 10 1020.001
0.005
0.010
0.050
0.100
0.500
1
M/M����
f
EG
F
WDNS
K
MLmLQPT
�
We applied this to these constrain “curtain”:
More Systematic Study —Results
-0.2-0.4
-0.6-0.8
-1
-2-3
-4-5
-6
-15 -10 -5 0
0.5
1.0
1.5
2.0
Log10(Mf/M�)���
�f
Log10(f)
-5
-3
-1
0
Words of Caution
One may wonder how the constraints on the PBH dark-matter fraction constrain the primordial power spectrum.
1016 1026 1036 104610-29
10-24
10-19
10-14
10-9
10-4
10-17 10-7 103 1013
M/g 11
�'
M/M� 11
Eva-poration
Neutronstars
Microlensing
WB DF
Words of Caution
One may wonder how the constraints on the PBH dark-matter fraction constrain the primordial power spectrum.
Go back to the constraints at the time of formation:
1016 1026 1036 104610-29
10-24
10-19
10-14
10-9
10-4
10-17 10-7 103 1013
M/g 11
�'
M/M� 11
Eva-poration
Neutronstars
Microlensing
WB DF
0.001 1 1000 1060.003
0.004
0.005
0.006
0.007
0.008
M/M�11
P�
Words of Caution
These constraints naïvely translate to:
Words of Caution
… drawing in the power spectrum of a running-mass model, which is perfectly d’accord with the mentioned constraints:
0.001 1 1000 1060.003
0.004
0.005
0.006
0.007
0.008
M/M�11
P�
0.001 1 1000 1060.003
0.004
0.005
0.006
0.007
0.008
M/M�11
P�
Words of Caution
Moreover, take the uncertainty due to non-sphericities into account:
Corpuscular Primordial Black Holes
Due to many semi-classical black hole paradoxes and mysteries, like information paradox, the exact thermality of Hawking radiation, the black hole’s negative heat capacity, …
Dvali and Gomez developed fully quantum framework for black holes and certain geometries.
being the for black holes or for cosmology.
Understand gravitational backgrounds, of characteristic wavelength ,, as states on Minkowski space of a certain occupation number of gravitons.
Corpuscular Gravity:Hawking Radiation
Hawking’s result at leading order in !
Note that particle creation is not a vacuum process!
Quantum depletion:
(in Planck units) or, with .
{ }
Corpuscular Primordial Black Holes
Now add baryons and consider the master equations:
gravitons
baryons
Baryon density increases till a critical value is reached.
Formation of a new state!
For … … the graviton depletion rate will be much larger than that of the baryons.
[Dvali-Gomez ’13]
Corpuscular Primordial Black Holes
Predictions (for ):
Mass:
Lowest possible mass of the bound state
Applied to astrophysical black-hole formation, using the same critical baryon density, and estimating .
Formation time:
which approximately reproduces the Chandrasekhar limit!
Conclusion
Conclusion
Primordial black holes are very interesting!
Conclusion
They are unique probes of various of their formation scenarios.
Primordial black holes are very interesting!
Conclusion
They are unique probes of various of their formation scenarios.
They could provide the dark matter.
Primordial black holes are very interesting!
Conclusion
They are unique probes of various of their formation scenarios.
They could provide the dark matter.
Though severely constrained, there are four possible windows their formation allowing for a significant fraction of the dark matter. The intermediate-mass one being the most topical, and the Planck-mass relics constituting ideal dark-matter candidates.
Primordial black holes are very interesting!
Conclusion
They are unique probes of various of their formation scenarios.
They could provide the dark matter.
Though severely constrained, there are four possible windows their formation allowing for a significant fraction of the dark matter. The intermediate-mass one being the most topical, and the Planck-mass relics constituting ideal dark-matter candidates.
A detailed understanding their formation is crucial.
Primordial black holes are very interesting!
Conclusion
They are unique probes of various of their formation scenarios.
They could provide the dark matter.
Though severely constrained, there are four possible windows their formation allowing for a significant fraction of the dark matter. The intermediate-mass one being the most topical, and the Planck-mass relics constituting ideal dark-matter candidates.
A detailed understanding their formation is crucial.
Extended mass spectra require special care when comparing to constraints.
Primordial black holes are very interesting!
[Carr]
The future will tell…
The future will tell…