The LISA forecast on a smooth crossover beyond the Standard Model through the scalar-induced gravitational waves

Supposing the Laser Interferometer Space Antenna (LISA) gravitational wave (GW) detector, we exhibit the detectability of a hypothetical smooth crossover in the early universe beyond the Standard Model of particle physics through the scalar-induced gravitational wave (SIGW) in terms of the Fisher forecast. A crossover at $\sim 100\mathrm{T}\mathrm{e}\mathrm{V}$ can leave a signal on the GW spectrum in the $\sim \mathrm{m}\mathrm{H}\mathrm{z}$ frequency range, the sweet spot of the LISA sensitivity. These possibilities are also interesting in the primordial black hole (PBH) context as the associated PBH mass $\sim {10}^{22}\mathrm{g}$ lies at the window to explain the whole dark matter. We found that the properties of the crossover can be well determined if the power spectrum of primordial scalar perturbations are as large as $\sim 5\times {10}^{-4}$ on the corresponding scale $\sim {10}^{12}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$.