Stasis Combs: Gravitational-Wave Signatures of Recurrent Cosmological Stasis

RESUMO

Cosmological stasis can recur multiple times, and each occurrence imprints a characteristic feature on the inflationary gravitational wave background (IGWB). We extend the single-epoch spectral template to an arbitrary number $N$ of consecutive stasis epochs, deriving a closed-form $N$-epoch piecewise template that factorizes cleanly: the amplitude steps at each break are determined entirely by the local equation of state $w_s^{(i)}$ of that epoch, while the inter-epoch plateau levels encode the accumulated spectral tilt from all prior epochs. Each resolved spectral feature yields an independent test of the Bessel-function consistency relation $C^2 = C^2(\alpha)$ established in~\cite{BarenboimBurns:paper1}, and the probability that $N$ such tests are simultaneously satisfied by a non-stasis spectrum falls sharply with $N$, making a confirmed multi-epoch comb the strongest available discriminator against constant-$w$ alternatives. We apply the formalism to the triple-stasis scenario of~\cite{Dienes:2023ziv}, which chains three pairwise stasis mechanisms (matter/radiation, vacuum-energy/matter, vacuum-energy/radiation) sequentially. For each block we derive the conditions under which the epoch lies within the template's validity range $w_s > -1/3$. We show that the Fig.~3 benchmark of~\cite{Dienes:2023ziv} falls outside this range and identify parameter choices that are both physically realizable and accessible to the template. We validate the inter-plateau ratio predictions numerically for representative two- and three-block chains, and work out the touching-epoch limit in which consecutive blocks share a break frequency without an intervening radiation-dominated interval. Finally, we discuss the detectability of a variety of multi-epoch stasis scenarios and give the minimum detectable tensor-to-scalar ratio as a function of the number of recurrent stasis epochs.