Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 122
forces and the fluctuations self–gravity. For a radiation–dominated Universe
there is an approximate equality between the Jeans mass, MJ, and the horizon
mass, MH. For a fluctuation exceding a critical threshold δc at horizon crossing,
gravity dominates and a PBH forms. On the other hand, a fluctuation with
δ < δc is dispersed by pressure forces (e.g. Jedamzik & Niemeyer, 1999).
The pressure response of a radiation fluid is given by equation (14). Any
decrease of the pressure response of the radiation fluid may yield a reduction
of the threshold δc. Such a behaviour is expected to occur during cosmological
first–order phase transitions (e.g. Jedamzik & Niemeyer, 1999).
A reduction of the PBH formation threshold for fluctuations which enter the
cosmological horizon during first–order phase transitions may have cosmological
implications, even if only modest. The slightest reduction of δc may result in
the formation of PBHs with masses of the order of the horizon mass during the
first–order phase transition, yielding a highly peaked PBH mass function (e.g.
Jedamzik & Niemeyer, 1999).
Jedamzik & Niemeyer (1999) studied the evolution of density fluctuations
upon horizon crossing during a cosmological first–order phase transition. In Figure
48 we show, as an example, the evolution of the radial energy density profile
of a fluctuation, with overdensity δ =0.535, from the initial horizon crossing
time t0 to 20.1t0. The fluctuations self–gravity exceeds pressure forces such that
the fluctuation separates from the Hubble flow and recollapses to high–energy
densities at the center until an event horizon forms (t ≈ 5t0). The resulting
young PBH rapidly increases its mass up to MP BH ≈ 0.06MH(t0) (t ≈ 5.5t0).
Subsequent accretion of material on the young PBH continues until the immense
pressure gradients close to the event horizon launch an outgoing pressure wave
which significantly dilutes the PBH environment. Accretion thereafter is negligible.
As a result we have, in this example, the formation of a PBH with initial
mass MP BH ≈ 0.34MH(t0).
The existence of a phase transition facilitates the PBH formation process as
is evident from Figure 49. Figure 49 is a zoom into the core of the fluctuation
shown in Figure 48. For comparison, this figure also shows the evolution of
a fluctuation with the same initial conditions, but entering the cosmological
horizon during an ordinary radiation–dominated epoch, by the dotted line. The
strong pressure gradients experienced by the fluctuation entering the horizon
during an epoch with EoS p = ρ/3 prevent, in this case, the formation of a PBH
(Jedamzik & Niemeyer, 1999).