Primordial Black Holes from Sound Speed Resonance during Inflation

TL;DR

A novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation ofPrimordial black holes in the early Universe is reported.

Abstract

We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe. For a general inflaton field, it can seed primordial density fluctuations and their propagation is governed by a parameter of sound speed square. Once if this parameter achieves an oscillatory feature for a while during inflation, a significant non-perturbative resonance effect on the inflaton field fluctuations takes place around a critical length scale, which results in significant peaks in the primordial power spectrum. By virtue of this robust mechanism, primordial black holes with specific mass function can be produced with a sufficient abundance for dark matter in sizable parameter ranges.

Figures (4)

• Figure 1: Parametric amplification of the resonating $k_*$ mode. The conformal time evolves from right to left. Numerical solutions under dS approximation and in the Starobinsky inflation model are given by the blue solid curve and the grey dashed line, respectively. The green line is the analytical profile of Eq. \ref{['profile']}, and the orange line represents a mode $k \neq k_*$ that is not resonating. The vertical dotted line depicts the time of Hubble-crossing for the $k_*$ mode.
• Figure 2: The power spectrum of primordial curvature perturbations with sharp peaks caused by sound speed resonance, and the comparison with various observational windows Bringmann:2011ut. The first peak around the resonating mode $k_*=7\times10^{9} ~\text{Mpc}^{-1}$ is the most significant one, while others at subsequent harmonics $2k_*$, $3k_*$, $4k_*$$...$ are sub-dominant by at least two orders of magnitude.
• Figure 3: Estimations for the fraction of PBHs against the total DM density, $f_\text{PBH}$, produced by sound speed resonance, for different values of $k_*$. Constraints from a number of astronomical experiments are also shown (see main text for refs.): their observational sensitivities are given by colored shadow areas. We choose $\xi = 0.1$ as well as a group of typical values for the rest parameters: $\gamma=0.2$, $g_{\text{form}} \simeq 100$, $\delta_c=0.37$, $n_s=0.968$.
• Figure 4: Constraints on the parameter space of sound speed resonance from various astronomical experiments shown in Fig. \ref{['fig:fPBHPlot1']}. The white regime is excluded since the enhancement yields $\zeta(k_*) >1$ which breaks the perturbation theory.