Non-linear Dynamics and Primordial Black Hole Formation During Kination

Abstract

We investigate the effects of large scalar inhomogeneities during the kination epoch, a period in which the universe's dynamics are dominated by the kinetic energy of a scalar field, by fully evolving the Einstein equations using numerical relativity. By tracking the non-linear growth of scalar perturbations with both sub-horizon and super-horizon initial wavelengths, we are able to compare their evolution to perturbative results. Our key findings show that in the deep sub-horizon limit, the perturbative behaviour remains valid, whereas in the super-horizon regime, non-linear dynamics exhibit a much richer phenomenology. Finally, we discuss the possibility of primordial black hole formation from the collapse of such perturbations and assess whether this process could serve as a viable mechanism to reheat the universe in the post-inflationary era.

Figures (9)

• Figure 1: Simulation results with initial gradient and kinetic perturbation in red and blue, respectively, for $\lambda_0=0.01H_0^{-1}$, $\delta_{0}=0.1$ -- at $N\sim 1.2$, the "perturbation" energy $\rho_{\delta \phi}$ dominates over the "background" energy density, but the two "components" still evolve as $a^{-4}$ and $a^{-6}$ respectively. The source of the initial perturbation energy density is indistinguishable to the system as long as they are of sub-horizon. Upper panel: the evolution of volume-averaged energy densities of the background and perturbation. Lower panel: background and perturbation energy densities as a power law of the volume-averaged scale factor $a\approx\langle \chi\rangle^{-1/2}$.
• Figure 2: Simulation results for $\lambda_0=1\times10^3H_0^{-1}$, $\delta_{0}=1\times10^{-10}$. The perturbation energy density is closely tracked by the gradient energy density and evolve as $\langle \rho_{\delta\phi}\rangle\sim\langle \rho_{\nabla}\rangle\sim a^{-2}$ while the kination background remains at $\overline{\rho}\sim a^{-6}$. Upper panel: the evolution of volume-averaged energy densities of the background, the gradient, and perturbations, Lower panel: background, gradient, and perturbation energy densities as a power law of the volume-averaged scale factor $a\approx\langle \chi\rangle^{-1/2}$.
• Figure 3: Simulation results for $\lambda_0=20H_0^{-1}$, $\delta_{0}=5\times10^{-4}$. The formation of black hole is indicated by the discontinuity around $\log(a)\sim 1.9$ at the end of the plot. The perturbation energy density deviates upwards away from the perturbative description when the induced kinetic perturbation becomes comparable with the gradient perturbation energy density. Upper panel: the evolution of volume-averaged energy densities of the background, gradient, kinetic, and perturbations, Lower panel: The background, gradient, kinetic, and perturbation energy densities as a power law of the $\log$ of the volume-averaged scale factor $a\approx\langle \chi\rangle^{-1/2}$. Simulation movie: https://www.youtube.com/watch?v=0msEzENelt8
• Figure 4: Extrapolated critical overdensity from numerical simulations for primordial black hole formation compared with the prediction from the Press-Schechter formalism of gravitational collapse Bhattacharya_2020Heurtier_2023. The upper bound of the error bar corresponds the lowest amplitude tested with a black hole formation, whereas the lower bound of the error bar corresponds the highest amplitude tested without a black hole formation, and the solid blue line indicates the central value between the two bounds.
• Figure 5: The mass of the black holes from simulations at the time of formation and a power law fit $M_{BH}\approx0.001\times(\lambda_0H_0)^{2.3}$