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 .



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






Formation at early times; primordial black holes (PBHs)







Formation at early times; primordial black holes (PBHs)


Masses of primordial black holes:

Primordial Black Holes —Evaporation

Quantum Mechanics

General Relativity

Thermodynamics

Black-hole radiation[Hawking 1974]


Formation of primordial black holes

http://www.damtp.cam.ac.uk/research/gr/public/cs_top.html

Cosmic string loops


Formation of primordial black holes by

http://www.damtp.cam.ac.uk/research/gr/public/cs_phase.html

Cosmic string loops



Bubble collisions

by

Cosmic string loops



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



Pressure reduction

Large density perturbations

Bubble collisions

https://ned.ipac.caltech.edu/level5/Sept12/Kravtsov/Kravtsov3.html

by

Cosmic string loops



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


black holesprimordial

derive the PBH density parameter:




variance derive the PBH density parameter:

In the Gaußian case




separate universes






separate universes



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:




Quantum Gravity:

Early Universe: Baryogenesis, Nucleosynthesis, Reionisation, …




Quantum Gravity:


High-Energy Physics: Cosmological and galactic gamma-rays, …




Quantum Gravity:


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

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


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


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]


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



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.


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.


[Green 2016]


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 .

{ }


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]


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.


Conclusion


They could provide the dark matter.


Conclusion



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.


Conclusion




A detailed understanding their formation is crucial.


Conclusion




A detailed understanding their formation is crucial.

Extended mass spectra require special care when comparing to constraints.


[Carr]

The future will tell…

The future will tell…

P mor al Black Hol as Dark Ma er Cleveland 16th of May 2017 P!mor"al Black Hol# as Dark Ma$er Black...

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