Analytic Description of Primordial Black Hole Formation from Scalar Field Fragmentation

Abstract

Primordial black hole (PBH) formation is a more generic phenomenon than was once thought. The dynamics of a scalar field in inflationary universe can produce PBHs under mild assumptions regarding the scalar potential. In the early universe, light scalar fields develop large expectation values during inflation and subsequently relax to the minimum of the effective potential at a later time. During the relaxation process, an initially homogeneous scalar condensate can fragment into lumps via an instability similar to the gravitational (Jeans) instability, where the scalar self-interactions, rather than gravity, play the leading role. The fragmentation of the scalar field into lumps (e.g. Q-balls or oscillons) creates matter composed of relatively few heavy "particles", whose distribution is subject to significant fluctuations unconstrained by comic microwave background (CMB) observations and unrelated to the large-scale structure. If this matter component comes to temporarily dominate the energy density before the scalar lumps decay, PBHs can be efficiently produced during the temporary matter-dominated era. We develop a general analytic framework for description of PBH formation in this class of models. We highlight the differences between the scalar fragmentation scenario and other commonly considered PBH formation models. Given the existence of the Higgs field and the preponderance of scalar fields within supersymmetric and other models of new physics, PBHs constitute an appealing and plausible candidate for dark matter.