Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era

TL;DR

This work investigates PBH production during an early matter-dominated epoch, considering perturbations from either an inflaton with a running spectral index or a blue-tilted spectator field. The authors model the curvature power spectrum as a sum of two components and derive PBH formation probabilities during MD, linking them to the PBH mass function and present-day DM fraction. By translating PBH constraints into bounds on the power spectrum, they obtain limits on the inflaton running ${\rm d}n/{\rm d}{\rm ln}k$ (with ${\rm d}n/{\rm d}{\rm ln}k \lesssim 0.001$–$0.007$ depending on $T_{reh}$) and on the spectator-field spectral index $n_s$ as a function of the amplitude $A_s$, while highlighting that PBHs can, in principle, account for all DM in certain parameter spaces. The results demonstrate the potential of PBH observations to probe small-scale curvature perturbations and early-Universe reheating physics, with a note on a post-proof correction to a MD-era variance factor.

Abstract

We study production of primordial black holes (PBHs) during an early matter-dominated phase. As a source of perturbations, we consider either the inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides a significant contribution to the PBH production at small scales. First, we identify the region of the parameter space where a significant fraction of the observed dark matter can be produced, taking into account all current PBH constraints. Then, we present constraints on the amplitude and spectral index of the spectator field as a function of the reheating temperature. We also derive constraints on the running of the inflaton spectral index, ${\rm d}n/{\rm d}{\rm ln}k \lesssim -0.002$, which are comparable to those from the Planck satellite for a scenario where the spectator field is absent.

Figures (7)

• Figure 1: Contributions of the inflaton (black dashed line) and the spectator field (gray dashed line) to the total curvature power spectrum (black solid line). The thick and thin lines correspond to $(n_s,\alpha_s,A_s/A)=(1.6,0,0.01)$ and $(n_s,\alpha_s,A_s/A)=(2.1,-0.034,0.01)$, respectively.
• Figure 2: The upper panel shows the power spectrum for $n_s=3.22$, $\alpha_s=-0.131$, $A/A_s=0.1$, $T_{\rm reh}=6$ MeV and $a_{\rm reh}/a_{\rm md}=40$. The lower panel shows the corresponding PBH mass function. The smallest and largest modes which produce PBHs during the matter-dominated era are indicated in the upper panel by the vertical lines.
• Figure 3: The lines show the different constraint for a monochromatic PBH mass function. The purple region on the left is excluded by evaporation Carr:2009jm, the red region by femto-lensing of gamma-ray bursts Barnacka:2012bm, the brown region by neutron-star capture Capela:2013yf, the green region by white dwarf explosions Graham:2015apa, the blue, yellow and purple regions by microlensing results from Subaru Niikura:2017zjd, EROS Tisserand:2006zx, and MACHO Allsman:2000kg respectively, and the dark blue region by Planck Ali-Haimoud:2016mbv. The regions to the right of the dashed lines are excluded by survival of a stars in Segue I Koushiappas:2017chw and Eridanus II Brandt:2016aco, and distribution of wide binaries Monroy-Rodriguez:2014ula. PBHs to the left of the gray vertical line have evaporated before today.
• Figure 4: Top panel: Minimum and maximum PBH masses. Black and gray lines correspond to $a_{\rm reh}/a_{\rm md}=40$ and $a_{\rm reh}/a_{\rm md}=100$, respectively. The red region is excluded by the BBN constraint on the reheating temperature. Bottom panel: The red contours correspond to 100% (upper) and 1% (lower) of PBH DM. The dark and light gray regions are excluded without and with dynamical constraints, respectively. The dashed contours from left to right correspond to $M_{\rm max}=30M_{\odot}$, $100M_{\odot}$ and $300M_{\odot}$. In both plots the values used in Fig. \ref{['ex']} are depicted by the solid gray lines and other parameters are fixed to the same values.
• Figure 5: Constraints on the amplitude of power spectrum. The gray dashed line corresponds to PBH production in a radiation-dominated era and the red lines in a matter-dominated era for reheating temperatures $10^5$ GeV, $30$ GeV and $0.01$ GeV from darkest to lightest. The red dashed lines show the smallest $k$ which become non-linear during the matter-dominated era, and the vertical black dashed lines the largest $k$ which cross the horizon after reheating. The black solid lines show the power spectrum with (thin) and without (thick) the spectator field. For the thin line the running of both the inflaton and spectator spectral indices are fixed to zero and the amplitude of the spectator field power spectrum to $A_s=0.1A$. Here the constraints in the matter-dominated era are calculated without the factor $\sigma^{3/2}$.