Effect of Primordial Black Holes on the Cosmic Microwave Background and Cosmological Parameter Estimates

TL;DR

This work demonstrates that a population of non-evaporating primordial black holes (PBHs) can inject energy into the early cosmic gas through gas accretion, altering the ionization and thermal history prior to galaxy formation. By modeling dark-halo growth around PBHs, PBH proper motions, accretion physics, and feedback, the authors constrain PBH abundances using WMAP3 CMB data and FIRAS spectral distortions. They show that PBH-induced modifications to recombination can bias cosmological parameter estimates, notably $\tau_e$, $\sigma_8$, and $n_s$, and provide tight upper limits on PBH fractions for $M_{pbh}>0.1~M_\odot$. They also find that PBHs can elevate primordial $\mathrm{H_2}$ and promote early star formation, while local feedback is generally subdominant; intermediate-mass black holes ($100-1000~M_\odot$) remain plausible PBH candidates with interesting cosmological implications. Overall, the results constrain PBHs as a component of dark matter while highlighting broader consequences for early structure formation and CMB-based parameter inference.

Abstract

We investigate the effect of non-evaporating primordial black holes (PBHs) on the ionization and thermal history of the universe. X-rays emitted by gas accretion onto PBHs modify the cosmic recombination history, producing measurable effects on the spectrum and anisotropies of the Cosmic Microwave Background (CMB). Using the third-year WMAP data and FIRAS data we improve existing upper limits on the abundance of PBHs with masses >0.1 Msun by several orders of magnitude. Fitting WMAP3 data with cosmological models that do not allow for non-standard recombination histories, as produced by PBHs or other early energy sources, may lead to an underestimate of the best-fit values of the amplitude of linear density fluctuations (sigma_8) and the scalar spectral index (n_s). Cosmological parameter estimates are affected because models with PBHs allow for larger values of the Thomson scattering optical depth, whose correlation with other parameters may not be correctly taken into account when PBHs are ignored. Values of tau_e=0.2, n_s=1 and sigma_8=0.9 are allowed at 95% CF. This result that may relieve recent tension between WMAP3 data and clusters data on the value of sigma_8. PBHs may increase the primordial molecular hydrogen abundance by up to two orders of magnitude, this promoting cooling and star formation. The suppression of galaxy formation due to X-ray heating is negligible for models consistent with the CMB data. Thus, the formation rate of the first galaxies and stars would be enhanced by a population of PBHs.

Figures (9)

• Figure 1: (Left). Ratio of the baryonic to dark matter power spectrum as a funtion of wavenumber $k$. Each curve, from bottom to the top, corresponds to scale factors $a=0.001, 0.002, 0.005, 0.01, 0.05, 0.1$, respectively. (Right). The solid curve shows the mean relative velocity between the dark matter and baryons in a sphere of comoving radius $r_0$. The dashed and dotted curves show the velocity dispersion within a sphere of comoving radius $r_0$ for the baryons and for the dark matter, respectively.
• Figure 2: Luminosity weighted effective velocity of PBHs (thick curves): $\langle v_{eff}\rangle_A$ (solid curve), is weighted assuming $l \propto \dot m^2$ and $\langle v_{eff}\rangle_B$ (dashed curve), is weighted assuming $l \propto \dot m$. See the text for details. The thin curves show the variance of the velocity distribution, $\langle V_{rel}\rangle$ (dashed line) and the gas sound speed, $c_s$ (dotted line), respectively.
• Figure 3: The dimensionless accretion rate of baryonic matter onto a "naked" PBH (without enveloping dark halo) as a function of redshift. The curves from bottom to top refers to $M_{pbh}=1, 10, 100, 300, 10^3, 10^4, 10^5$ M$_\odot$. The left panel is for a gas with electron fraction $x_e=10^{-3}$; the right panel for$x_e=1$. Here, thermal feedback and the contribution from PBHs inside virialized halos are neglected. The motion of the PBH due to linear density perturbations is included.
• Figure 4: Same as in Fig. \ref{['fig:A']} but including the growth of the dark halo surrounding the PBH ($\alpha=2.25$ and $\phi_i=3$). The curves from bottom to top refers to $M_{pbh}=1, 10, 100, 300, 10^3, 10^4, 10^5$ M$_\odot$.
• Figure 5: (a) Temperature structure of the H ii region around a PBH at $z=500$ emitting $S_0=10^{52}$ ionizing photons per second. The curves show the temperature profile after $2$ yr (dashed), $100$ yr (dotted) and $4600$ yr (solid) after the source turns on. The source spectrum is one appropriate for spherical accretion onto a black hole, with log-slope $\beta=0.5$.