Yonadav Barry Ginat

Abstract:

The matter power spectrum, $P(k)$ , is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in $d$ spatial dimensions, $P(k)$ has a universal $k^{-d}$ asymptotic scaling with the wave number $k$ , for $k\gg k_{\mathrm{nl}}$ , where $k_{\mathrm{nl}}^{-1}$ denotes the length scale at which nonlinearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a nonperturbative analysis of the system’s phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and nonlinear time scales are balanced, and this balance dictates the $k$ dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The $k^{-d}$ scaling is also derived by expressing $P(k)$ as a phase-space integral in the framework of kinetic field theory, which is analyzed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function—its nonvanishing only on a $d$ -dimensional submanifold of phase space—underpins both approaches. The theory is accompanied by 1D Vlasov-Poisson simulations, which confirm it.

Abstract:

In multi-component dark matter models, a fraction f pbh of the dark matter could be in the form of primordial black holes (PBHs) with (sub)solar masses. Some would have formed binaries that presently trace the Milky Way halo of particle dark matter. We explore the gravitational wave (GW) signal produced by such a hypothetical population of Galactic PBH binaries and assess its detectability by the LISA experiment. For this purpose, we model the formation and evolution of early-type PBH binaries accounting for GW hardening and binary disruption in the Milky Way. Our analysis reveals that the present-day Galactic population of PBH binaries is characterized by very high orbital eccentricities |1-e| ≪ 1. For a PBH mass M pbh ∼ 0.1 - 1M ⊙, this yields a GW background that peaks in the millihertz frequency range where the LISA instrumental noise is minimum. While this signal remains below the LISA detection threshold for viable f pbh ≲ 0.01, future GW observatories such as DECIGO and BBO could detect it if 0.01 ≲ M pbh ≲ 0.1M ⊙. Furthermore, we anticipate that, after 5 years of observations, LISA should be able to detect 𝒪(100) (resp. 𝒪(1)) loud Galactic PBH binaries of mass M pbh ≲ 0.1 - 1M ⊙ with a SNR ≥ 5 if f pbh = 0.01 (resp. f pbh = 0.001). Nonlinear effects not considered here such as mass accretion and dynamical capture could alter these predictions.