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\it \textbf{Left Panel}: Threshold $\mathcal{C}_{\rm th}$ (red solid) and shape parameter $\alpha_{\rm s}$ (blue dashed) values for different widths $\Delta$ of a log-normal power spectrum. \textbf{Right Panel}: The corresponding evolution of the threshold $\mathcal{C}^{\rm ew}_{\rm th}$ during the EW phase transition for different values of the shape parameter $\alpha_{\rm s}$, normalised with respect to the value of $\mathcal{C}_{\rm th}$ in the standard radiation dominated era.
\it Power-law-integrated sensitivity curves (solid lines) of LLR, eLO and eSLR~\cite{Foster:2025nzf}. We also show the first 14 bins of NANOGrav 15 yrs experiment~\cite{NANOGrav:2023gor,NANOGrav:2023hvm} and future sensitivity (dashed lines) for planned experiments like SKA~\cite{Zhao:2013bba,Babak:2024yhu} and LISA~\cite{LISA:2022kgy} and AION-km~\cite{Badurina:2019hst,Badurina:2021rgt,Abdalla:2024sst}. For completeness, we also show in black the SIGW spectra for two benchmark scenarios, with $A=10^{-2}$, $k_{\star}=10^9$ Mpc$^{-1}$, $\Delta=0.1$ (solid) and $\Delta=1$ (dashed).
\it Prospects from LLR, eLO and eSLR experiments based on the predicted sensitivity, which provide an upper bound on the power spectrum amplitude $A$ in case no signal is observed for different spectral shape $\Delta$ in the case of a log-normal power spectrum.
\it \textbf{Left Panel}: The implied upper limits on PBH abundance using the threshold statistics formalism. The orange and pink regions are respectively the 95\% CL allowed region of PBH abundance, obtained by microlensing events in the OGLE+HSC\,\cite{Niikura:2017zjd,Mroz:2017mvf,Niikura:2019kqi} (orange) (see also~\cite{Sugiyama:2021xqg}) and in the HSC \,\cite{Sugiyama:2026kpv} (pink) data due to the potential existence of PBHs. \textbf{Right Panel}: As in the left panel, but with PBH abundances calculated via the peak theory formalism.
\it Evolution of the squared sound speed, $c_s^2$, and the equation of state parameter $w(T)\equiv p/\rho$ during the EW phase transition as a function of the cosmological horizon mass $M_{ k}$ in units of a solar mass.