Gravitational Wave Signatures of Cosmological Stasis: A Unified Spectral Template

Abstract

Proposed in 2022 by Dienes et al., stasis is a dynamical fixed point in the early universe in which the equation of state, $w_s$, is fixed at a constant value. In this study we show that the inflationary gravitational wave imprint of any stasis epoch is captured by a closed-form spectral template controlled by two physical inputs, the equation of state $w_s$ and the stasis duration $\Delta N_\mathrm{stasis}$, that applies uniformly across every microphysical realization. The template presented here yields two independently measurable observables, the spectral tilt of the spectra in the stasis band, $\alpha(w_s)$ and the amplitude step $C^2(w_s)$ at the beginning and end of the stasis band. Eliminating $w_s$ gives a one-parameter consistency curve $C^2 = C^2(\alpha)$ on which the data must lie if the underlying cosmology is any constant-$w$ era. This makes the spectrum falsifiable without knowing $w_s$ in advance: a measured $(\alpha, C^2)$ pair either lands on the curve or rules out the constant-$w$ class. We show that BBO and DECIGO can resolve the perpendicular displacement from the consistency curve to $\sigma_\perp \simeq 1.5\times10^{-5}$ at a tensor-to-scalar ratio, $r = 0.01$, four orders of magnitude below the curve's range in $C^2$ meaning that any off-curve deviation is detectable across a broad range of allowed $r$ values.