Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls

We present a novel $\mathit{\text{gauge-invariant}}\mathit{\text{and}}\mathit{\text{minimal}}$ formation mechanism of primordial black holes (PBHs) in first-order phase transition (FOPT) and domain walls (DW) separately. This is based on the first-order tensor perturbations, generated during FOPT from bubble collisions & sound waves, and from DW annihilation, sourcing curvature, at second-order in perturbation theory. We show that the PBH formation implies $\mathit{\text{model-independent}}\mathit{\text{constraints}}$ on FOPT parameters ($\beta \mathrm{/}H,\alpha ,T_{\star }$ ) and on DW parameters, (${\alpha }_{\mathrm{a}\mathrm{n}\mathrm{n}},V_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}},\sigma$), from existing PBH constraints. We find that asteroid mass PBHs can become the entire dark matter (DM) of the Universe, for $T_{\star }\in (4\times {10}^2,{10}^4)$ GeV, for $\beta \mathrm{/}H\simeq 6$, involving $\alpha >\mathcal{O}(1)$ values. The corresponding FOPT Gravitational Waves (GW) amplitude will have its characteristic peak at ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}^{\mathrm{p}}{h}^2$ $\sim \mathcal{O}({10}^{-8})$ between frequencies $f_{\mathrm{p}}\in ({10}^{-5},{10}^{-2})$ Hz which is within the reach in LISA and SKA detectors. PBH as entire DM is possible for ${\sigma }^{1\mathrm{/}3}\in [{10}^6,{10}^8]$ TeV, for $V_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}^{1\mathrm{/}4}\in [{10}^7,{10}^{10}]$ MeV with the corresponding GW amplitude peak from DW annihilation ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}^{\mathrm{p}}{h}^2$ $\sim \mathcal{O}({10}^{-9})$ (for ${\alpha }_{\mathrm{a}\mathrm{n}\mathrm{n}}\sim {10}^{-2}$) and peak frequencies between $f_{\mathrm{p}}\in (4\times {10}^{-4},{10}^{-1})$ Hz with ($T_{\mathrm{a}\mathrm{n}\mathrm{n}}\in 4.5\times [{10}^3,{10}^6]$) GeV within the reach in LISA and ET detectors. We also provide semi-analytical formulae for the tensor-induced density spectrum, $P_{{\delta }^{(2)}}$, $M_{\mathrm{P}\mathrm{B}\mathrm{H}}$ and $f_{\mathrm{P}\mathrm{B}\mathrm{H}}$, relating them in terms of FOPT and DW parameters which in turn, are related to viable particle physics origin of such FOPT and DW, and therefore, constrain such microphysics, either in the visible, or in dark sector models.