Primordial Black Hole production in Critical Higgs Inflation

Abstract

Primordial Black Holes (PBH) arise naturally from high peaks in the curvature power spectrum of near-inflection-point single-field inflation, and could constitute today the dominant component of the dark matter in the universe. In this letter we explore the possibility that a broad spectrum of PBH is formed in models of Critical Higgs Inflation (CHI), where the near-inflection point is related to the critical value of the RGE running of both the Higgs self-coupling $λ(μ)$ and its non-minimal coupling to gravity $ξ(μ)$. We show that, for a wide range of model parameters, a half-domed-shaped peak in the matter spectrum arises at sufficiently small scales that it passes all the constraints from large scale structure observations. The predicted cosmic microwave background spectrum at large scales is in agreement with Planck 2015 data, and has a relatively large tensor-to-scalar ratio that may soon be detected by B-mode polarization experiments. Moreover, the wide peak in the power spectrum gives an approximately lognormal PBH distribution in the range of masses $0.01 - 100\,M_\odot$, which could explain the LIGO merger events, while passing all present PBH observational constraints. The stochastic background of gravitational waves coming from the unresolved black-hole-binary mergers could also be detected by LISA or PTA. Furthermore, the parameters of the CHI model are consistent, within $2σ$, with the measured Higgs parameters at the LHC and their running. Future measurements of the PBH mass spectrum could allow us to obtain complementary information about the Higgs couplings at energies well above the EW scale, and thus constrain new physics beyond the Standard Model.

Figures (3)

• Figure 1: Top panels: the Critical Higgs Inflation potential (left) and its curvature power spectrum ${\cal P}_{_{\cal R}}(N)$ (right). The large and broad half-dome peak at small scales ($N<\Delta N$) is responsible for PBH production over a wide range of masses. Bottom panels: evolution of the number of $e$-folds (left) and the slow-roll parameters (right) for the exact equations of motion.
• Figure 2: Left-panel:$(n_s,\,r)$-plane of CHI. The region with denser color corresponds to $\Delta N\in(30,35)$ and the contours represents the 1 and $2\sigma$ Planck constraints for models with variable $n_s$, $dn_s/d\ln k$ and $r$, obtained from the Planck Legacy Archive. Right panel: height of the peak as a function of its width. In both cases, the star corresponds to the reference parameter choice with $n_s=0.952$, $r=0.043$, $\Delta N=33.5$ and ${\cal P}_{_{\cal R}}(x_{\mathrm{max}})/{\cal P}_{_{\cal R}}(x_{65})= 2.3\times 10^{4}$ and the other points are all within $\beta\in(0.1 - 9)\times10^{-4}$ and $\Delta N\in(10,45)$.
• Figure 3: Present constraints on PBH from Extragalactic Gamma Background (EGB), femto-lensing of GRB, micro-lensing (HSC, Kepler, MACHO and EROS), Wide Binaries (WB), Eridanus II (Eri-II) and the CMB (FIRAS and Planck). See Refs. JGBCarr:2016drxCarr:2017jsz for a review. The primordial black holes (dashed-dotted line) produced in Critical Higgs Inflation could comprise all of the dark matter and still pass current constraints. Note that a relatively narrow mass distribution of PBH does not change appreciably the constraints (dashed gray line).