Nonlinear Matter Power Spectrum from relativistic $N$-body Simulations: ${\Lambda }_{\mathrm{s}}$CDM versus $\Lambda$CDM

Abstract

We present relativistic $N$-body simulations of a ${\Lambda }_{\mathrm{s}}$CDM - sign-switching cosmological constant (CC) - scenario under general relativity and compare its nonlinear matter power spectrum to $\Lambda$CDM at $z=15,2,1,0$, using best-fit parameters from Planck-only and a combined ''full'' dataset. During the AdS-like CC (${\Lambda }_{\mathrm{s}}<0$) phase, prior to the transition redshift $z_{†}$, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC (${\Lambda }_{\mathrm{s}}>0$), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio $P_{{\Lambda }_{\mathrm{s}}\mathrm{CDM}}/P_{\Lambda \mathrm{CDM}}$ exhibits a pronounced, redshift-dependent shape feature: a crest peaking at $\sim 20-25\%$ 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 $\sim 15-20\%$ uplift at $k\simeq 0.6-1.0h{\mathrm{Mpc}}^{-1}$. These wavenumbers correspond to group or poor-cluster environments and lie within the sensitivity range of weak lensing, galaxy-galaxy lensing, cluster counts, and tSZ 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.

18 pages, 8 figures, and 1 table

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