Abstract
We propose a model of inflation capable of generating a population of light black holes (about $10^{-16}$ - $10^{-14}$ solar masses) that might account for a significant fraction of the dark matter in the Universe. The effective potential of the model features an approximate inflection point arising from two-loop order logarithmic corrections in well-motivated and perturbative particle physics examples. This feature decelerates the inflaton before the end of inflation, enhancing the primordial spectrum of scalar fluctuations and triggering efficient black hole production with a peaked mass distribution. At larger field values, inflation occurs thanks to a generic small coupling between the inflaton and the curvature of spacetime. We compute accurately the peak mass and abundance of the primordial black holes using the Press-Schechter and Mukhanov-Sasaki formalisms, showing that the slow-roll approximation fails to reproduce the correct results by orders of magnitude. We study as well a qualitatively similar implementation of the idea, where the approximate inflection point is due to competing terms in a generic polynomial potential. In both models, requiring a significant part of the dark matter abundance to be in the form of black holes implies a small blue scalar tilt with a sizable negative running and a tensor spectrum that may be detected by the next-generation probes of the cosmic microwave background. We also comment on previous works on the topic.
Highlights
Soon after the first detection of gravitational waves (GW) emitted by a binary black hole (BH) merger [1], the possibility that BHs could constitute a significant amount of the Universe’s dark matter (DM) started to regain attention swiftly
We find that imposing the Planck cosmic microwave background (CMB) constraints and requiring a reasonable number of e-folds of inflation, these models can generate a population of PBHs that falls in the low-mass window (∼10−16.5–10−13 M⊙) that is potentially interesting for DM
In order to take seriously this idea, a mechanism operating before the time of nucleosynthesis that is able to generate a large abundance of PBHs with adequate masses is required
Summary
Soon after the first detection of gravitational waves (GW) emitted by a binary black hole (BH) merger [1], the possibility that BHs could constitute a significant amount of the Universe’s dark matter (DM) started to regain attention swiftly. If we assume that the potential V is nearly constant during inflation (which is the case in standard slow-roll, leading to a quasi-de Sitter universe), the expression (1.2) tells that the required enhancement of As may be achieved by significantly reducing the value of the slow-roll parameter εV Since this parameter quantifies the flatness of the potential, PBHs are produced provided that the rolling field encounters a sufficiently flat region of the potential during the course of inflation, which generates a peak in the spectrum of primordial fluctuations. The potential must be sufficiently flat for large values of the field (where the primordial spectrum observed with the CMB is generated) to satisfy the constraint (1.5) It must have an approximate plateau at smaller field values (corresponding to larger values of k) to produce PBHs and, a minimum with V 1⁄4 0 to reheat the Universe after inflation ends.
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