Abstract
Evidence for the primordial black holes (PBH) presence in the early Universe renews permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known models is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is the multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage. Analytical formulas have been developed that contain both quantum and classical contributions.
Highlights
Interest in the primordial black holes (PBHs) is dramatically increasing since the gravitational waves discovery from the black holes mergers (Abbott, 2016)
We continue elaboration of the model based on the second type phase transitions during the inflationary epoch (Rubin et al, 2000; Rubin et al, 2001; Khlopov et al, 2002)
We have shown that the mechanism of PBHs formation in the second-order phase transitions of scalar fields might produce a wide variety of the PBH mass spectra
Summary
Interest in the primordial black holes (PBHs) is dramatically increasing since the gravitational waves discovery from the black holes mergers (Abbott, 2016). There are a lot of models that contain a complicated form of scalar field potential. The discussed mechanism of PBHs production requires closed domain walls formation due to the quantum fluctuations of scalar fields at the inflation epoch (Rubin et al, 2000; Rubin et al, 2001). Substituting this solution into the integral in the exponent of the expression (12) one obtains the desired probability in the saddle point approximation dP φ2, t2; φ1, t1 const dφ exp. The probability for the field value F (the distribution function f) is obtained by substitution φ(t) Φ(t) − Φcl(t) into the formula above. We choose a part of phase space containing two maxima and at least one saddle point
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