Formation of subhorizon black holes from preheating

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to subhorizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press–Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

Figure 1

Time evolution of occupation number $n_k$ as defined in Eq. (2). The large value of $n_k$ justifies the classic treatment of inhomogeneities in our problem. The top line represent a mode that started outside of the horizon, and middle and lower lines refer to modes that remained inside the horizon at the end of inflation.

Figure 2

Time evolution of the equation of state $w$ for case I (top) and case II (bottom). Only for the latter $w$ steadily converges toward a constant value. See the text for more details.

Figure 3

Time evolution of the mean amplitude of ${\zeta }_k(t)$ as a function of the wave number $k$. Note the development of a maximum for a particular scale is formed inside the initial cosmological horizon scale $L_{H0}=1/H_0$.

Figure 4

Probability distribution function of ${\zeta }_k(t)$ for two modes at different times of evolution in case I. The top (bottom) panel represents the PDF for a mode $L_H(t_{\text{f}})/L=46$ ($L_H(t_{\mathrm{f}})/L=23$) at the end of the simulation when $a(t_f)=30$. Note that the shape of the distribution evolves with time through the preheating phase generating negatively skewed distributions.

Figure 5

Same as Fig. 4 but for the model of case II. In this case, the distributions are positively skewed, a feature that favors the formation of PBHs.

Figure 6

Tail of the PDF for the scale $L_H(t_{\mathrm{f}})/L=23$. The true normalized distribution is approximated by two analytical PDFs. From below, the skewed normal distribution, and from above, the closest approximation is a Moyal distribution, which is the best approximation to the tail of the distribution.