Primordial Black Holes as Dark Matter and the Tachyonic Trap During Inflation

TL;DR

This work presents a multi-field inflation model in which a tachyonic trap at a Symmetry Breaking Point induces resonant production of a second field, creating a sharp small-scale peak in the curvature perturbation ${\cal P}_{\zeta}$. The amplified perturbations lead to the formation of primordial black holes (PBHs) with an asteroid-mass peak around $m_{PBH} \sim 3\times 10^{19}$ g, potentially accounting for all dark matter via $f_{PBH}\sim\mathcal{O}(1)$, while also sourcing stochastic induced gravitational waves (SIGWs) in the deci-Hz band detectable by future missions such as LISA, DECIGO, and BBO. PBHs formed in this scenario can form binaries and merge, producing an additional GW background accessible to resonant cavities and space-based detectors. The analysis ties early-Universe microphysics to observable gravitational-wave signals, offering a concrete, testable link between PBH dark matter and a rich multiband GW phenomenology.

Abstract

We show that resonant processes during multi-field inflation can generate a large curvature perturbation on small scales. This perturbation naturally leads to the formation of primordial black holes that may constitute dark matter, as well as to the production of stochastic induced gravitational waves in the deci-Hz band. Such waves are within reach of future space-based interferometers such as LISA, DECIGO and BBO. In addition, primordial black hole binaries formed at late times produce merger gravitational waves that can be probed by the resonant cavity experiments in addition to DECIGO and BBO.

Figures (10)

• Figure 1: Rescaled RMI potential $U\left(\phi\right)$ in Eq. (\ref{['Udef']}) for several $\alpha$, $A$ and $B$ values.
• Figure 2: The numerical solution of homogeneous RMI equations ("Exact"). At the pivot scale, on the RHS of the plot, inflation is well approximated by slow-roll (cf. Eq. (\ref{['sr']})), but eventually it enters the ultra-slow-roll regime (cf. Eq. (\ref{['usr']})). Conventionally this transition is taken at $\eta=1$ (vertical gray line).
• Figure 3: Parameter regions for several different $\alpha$ values where the running mass inflation models are compatible with the CMB constraints on the primordial spectrum at the pivot scale $k_*=0.05\,\mathrm{Mpc}^{-1}$ (Eqs. (\ref{['ns-const']})--(\ref{['r-const']})). We also impose two other conditions: $\phi_{*}<m_{\mathrm{Pl}}$ when the pivot scale exits the horizon and that the energy scale of inflation is larger than the Big Bang Nucleosynthesis (BBN) scale.
• Figure 4: Schematic depiction of our scenario. At stage 1 the field rolls down along the RMI direction (blue curve). At tree level, the linear potential (red curve) does not exist. Once the field reaches SBP (stage 2) it resonantly excites the $\chi$ field. Excitations backreact onto the motion of the field, which can be effectively described by a steepening linear potential. At this stage the trapped $\phi$ field oscillates around $\phi_{\mathrm{SBP}}$ with an exponentially decreasing amplitude. Eventually the amplitude becomes too small to excite the $\chi$ field. At that point the evolution enters the 3rd stage, in which the field rolls down solely in the direction of the sufficiently flat waterfall potential (brown curve) with $\phi$ remaining being fixed at $\phi_\mathrm{SBP}$. During stage 2 the metric perturbation is also resonantly amplified for scales which exit the horizon at that time.
• Figure 5: The allowed range of the energy scale of inflation (green shaded region). Orange and blue lines represent bounds in Eqs. \ref{['V-lower']} and \ref{['V-upper']} respectively. The red dot marks the value of the model specified in section \ref{['subsec:numerical']}.