Isocurvature Constraints on Dark Matter from Evaporated Primordial Black Holes

Abstract

We revisit the scenario in which stable particles of a dark sector are produced through the complete evaporation of light primordial black holes (PBHs) formed in the early Universe. We investigate in detail the role of isocurvature perturbations that may arise in this framework. PBHs inherit Poisson fluctuations on unobservable small scales at formation; however, in the presence of primordial non-Gaussianity that couples long- and short-wavelength modes, these fluctuations can source isocurvature perturbations on cosmological scales. Such perturbations are unavoidably transferred to the dark sector particles emitted via Hawking evaporation. We highlight the potential impact of isocurvature constraints on dark sector particles produced through PBH evaporation. Along the way, we re-assess the constraints on this scenario arising from the overproduction of dark matter (DM), accounting for both PBH evaporation and gravitational production (freeze-in) during (after) inflation, as well as bounds from warm DM and the overproduction of scalar-induced gravitational waves.

Figures (5)

• Figure 1: Left: Parameter space where a DM particle is overproduced by inflationary production (considering a fermion or minimally-coupled scalar, in orange) or by UV freeze-in (in pink), for two values of $\epsilon_\text{\scriptsize RH}= T_\text{max}/T_\text{\scriptsize{inst.\,RH}}$. Below the dotted lines, these yields are Boltzmann-suppressed. Right: translation of these bounds to the minimum PBH mass that is achievable for a given $m_\text{DS}$.
• Figure 2: Variation of the linear bias $b_1$ as a function of the local-type non-Gaussianity parameter $f_\text{\scriptsize NL}$ for several values of $\log_{10}\beta$ (marked with different colors as shown in the legend). Solid (dashed) lines corresponding to positive (negative) $f_\text{\scriptsize NL}$ and $b_1$.
• Figure 3: Simplified version of \ref{['fig:DM_PBH']}, for the case $m_\text{DS} =10^7\,\text{GeV}$, to highlight the main features of the bounds. In green we show the overproduction bound, in cyan the more stringent bound from isocurvature perturbations assuming $f_\text{\scriptsize NL} = 10$. Above the purple diagonal curve, all the DM being in the DS from evaporated PBHs is excluded by Lyman-$\alpha$ bounds on warm DM, while points on the left of the vertical dashed lines are excluded by gravitational overproduction, depending on the assumed $\epsilon_{\rm RH}$.
• Figure 4: Values of $\beta$ , for given PBH mass $M_\text{PBH}^{\rm in}$ yielding the observed DM abundance for various values of $m_\text{DS}$. Each contour corresponds to $\Omega_{\rm DM} h^2 = 0.11$; points above (below) overproduce (underproduce) dark matter. Gray shaded regions are excluded by the maximum allowed $H$ (left), given the upper bound on the tensor-to-scalar-ratio $r$ (the PBH mass at formation being associated to the horizon mass), and by energy injection from evaporation at BBN (right). The triangular upper blue shaded region is excluded by SIGW emission overcoming the $\Delta N_{\rm eff}$ bound on the GW abundance.
• Figure 5: Same as \ref{['fig:DM_PBH']} but now showing the constraints as a function of $m_\text{DS}$ for different PBH masses.