Detecting cosmological stasis with future gravitational wave observatories

We map the observational predictions of cosmological stasis in the inflationary gravitational wave background onto the sensitivity bands of current and planned gravitational wave detectors. Using the closed-form piecewise spectral template derived in the companion paper, we generate detectability maps for four stasis scenarios: canonical, dynamical scalar, vacuum-energy/matter, and vacuum-energy/radiation across the frequency bands probed by NANOGrav, SKA, LISA, DECIGO, BBO, the Einstein Telescope, and Cosmic Explorer. For scenarios in which the spectrum is suppressed, $w_s < 1/3$, the stasis feature is detectable by BBO in the region of $(w_s,ΔN)$ parameter space in which $w_s\gtrsim 0.2$ for tensor-to-scalar ratios close to the Planck upper limit, r = 0.036. For scenarios in which the spectrum is enhanced, $w_s > 1/3$, the stasis feature is detectable by BBO across the entire $(w_s,ΔN)$ parameter space for tensor-to-scalar ratios of $O(0.01)$. We characterize the Standard Model (SM) $g_*$ fine structure of the IGWB, showing that SM phase transitions introduce spectral steps of $\approx 20\%$ (electroweak, at $\sim 2.6\times10^{-6}$~Hz) and $\approx 53\%$ (QCD, at $\sim 3.6\times 10^{-9}$~Hz). For stasis scenarios with end-of-stasis temperatures below the QCD scale these steps fall inside the stasis band and constitute additional spectral features that complement the primary signature. Finally, we model the finite-width end-of-stasis transition phenomenologically, demonstrating that the spectral break at $f_{end}$ is smoothed over a log-frequency window $ΔN_\mathrm{trans}\times 3(1+w_s)/4$, and that the consistency relation $C^2=C^2(α)$ remains testable provided $ΔN_\mathrm{stasis}\gg ΔN_\mathrm{trans}$, a condition easily satisfied for all scenarios of phenomenological interest.