We present relativistic $N$-body simulations of a ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$—sign-switching cosmological constant (CC)—scenario under general relativity and compare its nonlinear matter power spectrum to $\mathrm{\Lambda }\mathrm{CDM}$ at $z=15$, 2, 1, 0, using best-fit parameters from Planck-only and a combined “full” dataset. During the AdS-like CC (${\mathrm{\Lambda }}_{\mathrm{s}}<0$) phase, prior to the transition redshift $z_{†}$, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC (${\mathrm{\Lambda }}_{\mathrm{s}}>0$), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio $P_{{\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}}/P_{\mathrm{\Lambda }\mathrm{CDM}}$ exhibits a pronounced, redshift-dependent shape feature: a crest peaking at about 20%–25% around $k\simeq 1–3h{\mathrm{Mpc}}^{-1}$ near the transition, which then migrates to larger physical scales and persists to $z=0$ as a robust uplift of around 15%–20% at $k\simeq 0.6–1.0h{\mathrm{Mpc}}^{-1}$. 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 ${\sigma }_8$ or $S_8$. The timing (earlier for Planck-only, later for the full dataset) and the amplitude of the crest align with the “cosmic noon” epoch ($z\simeq 1–2$), offering a gravitational prior for the observed peak in the cosmic star-formation rate.

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• Cosmological parameters
• Cosmology
• Dark energy
• Evolution of the Universe