Primordial black holes within Higgs hybrid metric-Palatini approach

TL;DR

The paper investigates primordial black hole production during radiation domination in the Higgs hybrid metric-Palatini inflation framework, where the inflaton is non-minimally coupled to Palatini curvature and the Higgs potential is $V(φ)=(1/4)\λφ^4$. It computes the curvature power spectrum $P_R(k)$, maps PBH masses via $M_{PBH}(k)$, and evaluates the collapse fraction $\beta(M_{PBH})$ using a Gaussian window and $\delta_c\simeq 0.414$, with the abundance expressed as $f_{PBH}$. The results show a significant small-scale enhancement of $P_R(k)$ enabling PBH formation; for $\xi=10^{-4}$, $N=52$ or $55$ PBHs can constitute all of DM in a certain mass window, while for $\xi=10^{-4.1}$ they contribute a smaller fraction with heavier PBHs, illustrating a strong dependence on model parameters. The work links inflationary dynamics in a modified gravity context to DM phenomenology and observational constraints, highlighting parameter regions where PBHs plausibly explain all or part of the cosmic dark matter.

Abstract

In this paper, we investigate the production of primordial black holes (PBHs) during the radiation-dominated era. The collapse of significant density perturbations originating from large primordial scalar fluctuations generated during inflation can lead to the formation of primordial black holes. In our study, we adopt the Higgs hybrid metric-Palatini model as our framework, in which the inflaton field and the Palatini curvature are non-minimally coupled. To achieve our objective, we analyze the behavior of the primordial curvature power spectrum, which exhibits a large enhancement at small scales corresponding to large wavenumbers $k$. Furthermore, we examine the probability of PBHs formation by studying the mass variance, $σ(M_{PBH})$, and the mass fraction of the total energy density collapsing into PBHs, $β(M_{PBH})$. The evolution of both functions is consistent with current observational constraints. Finally, we investigate the abundance of primordial black holes as a dark matter candidate. We found that they can account for the totality or a fraction of the current dark matter content, depending primarily on the values of the coupling constant and the e-folds number.

Figures (6)

• Figure 1: Variation of the scalar spectral index versus the e-folding number for three different values of the coupling constant $\xi=10^{-3.9}$, $\xi=10^{-4.1}$ and $\xi=10^{-4.5}$. The gray region indicates the Planck bounds imposed on $n_s$.
• Figure 2: Evolution of the tensor-to-scalar, $r$, versus the spectral index, $n_s$, for different values of the coupling constant $\xi$, varying the e-folds number $N$ within the range $35\leq N\leq 75$.
• Figure 3: The primordial curvature power spectra, $P_{R}(k)$, as a function of the dimensionless ratio $k/k_{*}$. The blue and the green lines correspond to the value of e-folding number, $N=52$ and $N=55$, respectively. We consider two values of the coupling constant, $\xi=10^{-4}$ (left panel) and $\xi=10^{-4.1}$ (right panel). Here, the pivot scale is taken as $k_{*}=0.05$ Mpc$^{-1}$.
• Figure 4: The mass variance against the PBH mass, $M_{PBH}$, for $N=52$ and $N=55$ . Two values of the coupling constant are considered: $\xi=10^{-4}$ (left panel) and $\xi=10^{-4.1}$ (right panel). The dashed line represents the threshold $\sigma_{thresh}=0.08$ above which PBHs would be overproduced.
• Figure 5: The fraction of the total energy density collapsing into PBHs as a function of the PBH mass, considering two cases where $N=52, 55$. We consider two coupling constant values, specifically $\xi=10^{-4}$ (left panel) and $\xi=10^{-4.1}$ (right panel).