Primordial Black Holes and Cosmological Phase Transitions Report ...

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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).
PBHs and Cosmological Phase Transitions 123 Figure 48: Energy density, ɛ, as a function of scaled circumferential radius, Rsc =(R/Rk(t0))(a0/a), for a fluctuation with initial density contrast δ =0.535 at horizon crossing. The initial horizon at t0 is located at Rsc = 1. From top to bottom, solid lines show the fluctuation at 1., 1.22, 1.49, 1.82, 2.23, 2.72, 3.32, 4.06, 4.95, 6.05, 7.39, 9.03, 11.0, 13.5, 16.4, and 20.1 times the initial time t0. The two horizontal dotted lines indicate the regime of energy densities in which fluid elements exist within mixed phases. The formation of a PBH with Mpbh ≈ 0.34MH(t0) results (Jedamzik & Niemeyer, 1999). Figure 49: A zoom into the upper left region of Figure 48. From top to bottom, solid lines show the fluctuation at 1.0, 1.22, 1.49, 1.82, 2.22, 2.72, 3.32, 4.06, 4.95, and 5.47 times the initial time t0. The horizontal dashed lines indicate the energy densities at onset and completion of the phase transition. The dotted lines show, for comparison, the evolution of a fluctuation with the same initial fluctuation parameters, but entering the cosmological horizon during an epoch with EoS p = ρ/3 (Jedamzik & Niemeyer, 1999).
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CCM-Centro de Ciências Matemática
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Contents List of Figures vii List o
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PBHs and Cosmological Phase Transit
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List of Tables 1 The Universe timel
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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