1. Primordial Black Holes and Dark Matter? John Miller (Oxford) Collaborators: Ilia Musco (Oslo) Antonella Garzilli (SISSA)

2. 1 Contents of the Universe: Evidence from the CMB, supernovae, gravitational lensing, nucleosynthesis and motion of stars in galaxies  ~ 73% in dark energy ~ 23% in dark matter ~ 4% in atomic matter

3. 2 What makes up the dark matter? - we know that it’s “Non-Baryonic” in the sense that it mustn’t mess up cosmological nucleosynthesis - widely thought to be particles which are: - Weakly-Interacting (mainly gravity) & Cold(??) - main candidate: supersymmetric particles But could it be Primordial Black Holes (PBHs) formed < 1 min after the Big Bang?? - “standard” matter and radiation locked up in PBHs before nucleosynthesis

4. 3 Constraints from microlensing, etc : Allowed mass range for PBHs as significant dark matter - 10 17 – 10 26 g (r s ~ 100 fm – 10 -2 cm)

5. 4 Could we detect the “allowed” range by interactions with stars? - PBHs moving in the Galaxy with ~ virial velocity (2 x 10 7 cm/s) – could collide with stars - get interaction with stellar matter via dynamical friction  - brightening of star - asteroseismic disturbance - possible ignition of nuclear reactions How could so many PBHs with masses in this range be formed?

6. 5 Standard picture for the formation of cosmic structures - originated as small quantum fluctuations then inflated onto supra-horizon scales - subsequently come back inside the horizon again as the Universe continues to expand; they can then collapse - start on the supra-horizon scale as a mixture of growing and decaying modes in a linear regime - but the decaying modes soon become small, leaving just the growing modes - these are special types of perturbation

7. 6 Large-scale structure : - comes from perturbations re-entering the horizon in the matter-dominated era In the radiation-dominated era: - just 2 possibilities for re-entering perturbations: - those above a critical amplitude collapse to form black holes - smaller ones disperse into the background - PBHs formed from growing-modes follow a scaling law

8. 7 Scaling law for PBHs: What you get in PBHs depends on P(δ) - probably need help from a phase transition to temporarily soften the equation of state - mechanism might work but it looks difficult to get the right number of PBHs

9. 8 Conclusions - Having microscopic PBHs as the dark matter is not ruled out by present observations - Finding direct evidence for them is hard but not impossible - There is a plausible mechanism to form them but it looks difficult to get the right number - seems to need a continuous phase transition and the fluctuation spectral index n to increase suitably at small scales - Bottom line : Having PBHs as the dark matter is a very long shot, but is not ruled out and probably deserves further study

10. 9 Growing-mode perturbations - have a particular combination of density and velocity perturbation which makes them “hold together” as they evolve - define density and velocity perturbations δ e = (e – e b )/e b δ u = (U – U b )/U b - in the linear regime during the radiation-dominated era δ u ~ - (δ e /4) for a growing mode - typically have an over-density surrounded by a compensating under-density

11. 10 The wind and the void: