Nonlinear matter power spectrum from relativistic N-body simulations: Λ_sCDM versus ΛCDM

We present relativistic N-body simulations of a Λ_sCDM—sign-switching cosmological constant (CC)—scenario under general relativity and compare its nonlinear matter power spectrum to ΛCDM at z = 15, 2, 1, 0, using best-fit parameters from Planck-only and a combined “full” dataset. During the AdS-like CC (Λ₈ < 0) phase, prior to the transition redshift Zf, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC (Λ₈ > 0), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio Pa_sCdm=Pacdm exhibits a pronounced, redshift-dependent shape feature: a crest peaking at about 20%-25% around k (Formula presented.) 1-3h Mpc⁻¹ near the transition, which then migrates to larger physical scales and persists to z = 0 as a robust uplift of around 15%-20% at k (Formula presented.) 0.6-1.0h Mpc⁻¹. These wave numbers correspond to group or poor-cluster environments and lie within the sensitivity range of weak lensing, galaxy-galaxy lensing, cluster counts, and thermal Sunyaev-Zel'dovich power, providing a concrete, falsifiable target that cannot be mimicked by a scale-independent change in σ₈ or S₈. The timing (earlier for Planck-only, later for the full dataset) and the amplitude of the crest align with the “cosmic noon” epoch (z » 1-2), offering a gravitational prior for the observed peak in the cosmic star-formation rate.