Nonlinear Matter Power Spectrum from relativistic $N$-body Simulations: $Λ_{\rm s}$CDM versus $Λ$CDM

TL;DR

This paper investigates how a sign-switching cosmological constant model, Λ_sCDM, alters nonlinear structure formation relative to ΛCDM using fully relativistic N-body simulations with gevolution in GR. The AdS-like phase prior to a rapid AdS-to-dS transition suppresses Hubble friction and boosts perturbation growth, while the post-transition dS-like phase increases the expansion rate and dampens growth but preserves much of the prior amplification. The authors identify a distinctive, localized crest in the nonlinear matter power-spectrum ratio P_{Λ_sCDM}/P_{ΛCDM} that peaks near the transition at k ~ 1–3 h/Mpc with amplitudes around 20–25%, then drifts to larger scales (k ~ 0.6–1.0 h/Mpc) by z = 0, with amplitudes ~15–20%, and whose location and strength depend on the data combination (Planck-only vs full). This crest occurs on group/poor-cluster scales and provides a falsifiable target for weak lensing, galaxy-galaxy lensing, cluster counts, and tSZ measurements, offering a gravitational prior tied to the cosmic noon epoch (~z = 1–2) and a potential route to alleviating growth-index tensions without modifying gravity.

Abstract

We present relativistic $N$-body simulations of a $Λ_{\rm s}$CDM - sign-switching cosmological constant (CC) - scenario under general relativity and compare its nonlinear matter power spectrum to $Λ$CDM at ${z = 15,\,2,\,1,\,0}$, using best-fit parameters from Planck-only and a combined ''full'' dataset. During the AdS-like CC ($Λ_{\rm s}<0$) phase, prior to the transition redshift $z_\dagger$, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC ($Λ_{\rm s}>0$), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio $P_{Λ_{\rm s}\rm CDM}/P_{Λ\rm CDM}$ exhibits a pronounced, redshift-dependent shape feature: a crest peaking at ${\sim 20-25\%}$ around ${k \simeq 1-3\,h\,\mathrm{Mpc}^{-1}}$ near the transition, which then migrates to larger physical scales and persists to ${z = 0}$ as a robust ${\sim 15-20\%}$ uplift at ${k \simeq 0.6-1.0\,h\,\mathrm{Mpc}^{-1}}$. These wavenumbers correspond to group/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 $σ_8$ 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.

Figures (6)

• Figure 1: Total-matter (baryons+CDM+massive $\nu$) power spectra from our gevolution simulations, shown for the Planck-only (left) and full (right) best-fit parameter sets at $z=15,2,1,0$. Colored solid curves correspond to $\Lambda_{\mathrm{s}}\mathrm{CDM}$, while black dash-dotted curves indicate $\Lambda\mathrm{CDM}$. Within each dataset, both runs share identical simulation and IC generation settings. Absolute spectra are plotted up to $k_{\rm f} = 1.6\,h\,\mathrm{Mpc}^{-1} \simeq k_{\rm Ny}/4$.
• Figure 2: Ratios of the total-matter power spectra, $P_{\Lambda_{\rm s}\mathrm{CDM}}/P_{\Lambda\mathrm{CDM}}$, at $z=15,2,1,0$ for the Planck-only (dashed) and full (solid) best-fit parameter sets. Vertical tick marks denote the $k$-locations of the local maxima from $z=2$ onward. Peak amplitudes are: Planck-only, $1.202$ at $z=2$, $1.186$ at $z=1$, $1.140$ at $z=0$; full dataset, $1.212$ at $z=2$, $1.248$ at $z=1$, $1.217$ at $z=0$.
• Figure 3: CDM-baryon (cb) power spectra from gevolution at $z=15,2,1,0$ for the Planck-only best-fit parameters. Dash-dotted curves show the corresponding linear predictions from CLASS in Newtonian gauge. Agreement is excellent on large scales, while deviations at higher $k$ reflect nonlinear clustering for $z \leq 2$.
• Figure 4: CDM-baryon (cb) power spectra from gevolution at $z=15,2,1,0$ for the full best-fit parameters. Dash-dotted curves show the corresponding linear predictions from CLASS in Newtonian gauge. As in the Planck-only case, excellent agreement is found on large scales between each $N$-body and linear prediction pair.
• Figure 5: Ratios of CDM--baryon (cb) power spectra, $P_{\Lambda_{\rm s}{\rm CDM}}/P_{\Lambda{\rm CDM}}$, at $z=15,2,1,0$ for the Planck-only best-fit parameters. A localized enhancement appears near the switch epoch and subsequently drifts to larger physical scales, reaching $k\!\sim\!0.6$–$1.0\,h\,\mathrm{Mpc}^{-1}$ by $z=0$. On linear scales the relative spectra from simulations agree with those from CLASS, as expected.