We recently showed that postulated ultracompact minihalos with a steep density profile do not form in realistic simulations with enhanced initial perturbations. In this paper we assume that a small fraction of the dark matter consists of primordial black holes (PBHs) and simulate the formation of structures around them. We find that in this scenario halos with steep density profiles do form, consistent with theoretical predictions. If the rest of the dark matter consists of weakly interacting massive particles (WIMPs), we also show that WIMPs in the dense innermost part of halos surrounding the PBH would annihilate and produce a detectable gamma-ray signal. The non-detection of this signal implies that PBHs make up at most one billionth of the dark matter, provided that their mass is greater than one millionth of the mass of the Sun. Similarly, a detection of PBHs would imply that the remaining dark matter could not be WIMPs.

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We perform three-dimensional simulations of structure formation in the early Universe, when boosting the primordial power spectrum on ∼kpc scales. We demonstrate that our simulations are capable of producing power-law profiles close to the steep ρ ∝ r −9=4 halo profiles that are commonly assumed to be a good approximation to ultracompact minihalos (UCMHs). However, we show that for more realistic initial conditions in which halos are neither perfectly symmetric nor isolated the steep power-law profile is disrupted, and we find that the Navarro-Frenk-White profile is a better fit to most halos. In the presence of background fluctuations, even extreme, nearly spherical initial conditions do not remain exceptional. Nonetheless, boosting the amplitude of initial fluctuations causes all structures to form earlier and thus at larger densities. With a sufficiently large amplitude of fluctuations, we find that values for the concentration of typical halos in our simulations can become very large. However, despite the signal coming from dark matter annihilation inside the cores of these halos being enhanced, it is still orders of magnitude smaller compared to the usually assumed UCMH profile. The upper bound on the primordial power spectrum from the nonobservation of UCMHs should therefore be reevaluated.

We chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schrödinger equation, where the small parameter acts as a softening scale that regulates singularities at shell-crossing. The leading-order propagator, called free propagator, is the semiclassical equivalent of the Zel'dovich approximation (ZA), that describes inertial particle motion along straight trajectories. At next-to-leading order, we solve for the propagator perturbatively and obtain, in the classical limit the displacement field from second-order Lagrangian perturbation theory (LPT). The associated velocity naturally includes an additional term that would be considered as third order in LPT. We show that this term is actually needed to preserve the underlying Hamiltonian structure, and ignoring it could lead to the spurious excitation of vorticity in certain implementations of second-order LPT. We show that for sufficiently small the corresponding propagator solutions closely resemble LPT, with the additions that spurious vorticity is avoided and the dynamics at shell-crossing is regularised. Our analytical results possess a symplectic structure that allows us to advance numerical schemes for the large-scale structure. For times shortly after shell-crossing, we explore the generation of vorticity, which in our method does not involve any explicit multi-stream averaging, but instead arises naturally as a conserved topological charge.