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arxiv: 2510.18741 · v2 · submitted 2025-10-21 · 🌌 astro-ph.CO · gr-qc

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

\"Ozg\"ur Akarsu , Eleonora Di Valentino , Ji\v{r}\'i Vysko\v{c}il , Ezgi Y{\i}lmaz , A. Emrah Y\"ukselci , Alexander Zhuk This is my paper

Pith reviewed 2026-05-18 04:42 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords cosmologydark energyN-body simulationsmatter power spectrumsign-switching cosmological constantnonlinear structure formationΛsCDM
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0 comments X

The pith

A sign-switching cosmological constant produces a distinct redshift-dependent crest in the nonlinear matter power spectrum ratio, peaking at 20-25 percent near the transition and leaving a lasting 15-20 percent uplift at z=0 on scales of k=

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper performs relativistic N-body simulations of the ΛsCDM model, in which the cosmological constant switches from negative to positive at a transition redshift z_†, and compares the resulting nonlinear matter power spectrum to that of standard ΛCDM. Before the switch the AdS-like phase reduces Hubble friction and accelerates the growth of density perturbations; after the switch the larger expansion rate only partly offsets this earlier amplification. The simulations reveal that the ratio of the two power spectra therefore develops a crest that reaches 20-25 percent near k=1-3 h Mpc^{-1} close to the transition, then migrates to larger physical scales while remaining visible at z=0 as a 15-20 percent excess near k=0.6-1 h Mpc^{-1}. These wavenumbers lie in the range probed by weak lensing, cluster counts and the thermal Sunyaev-Zel'dovich effect, and the timing of the crest coincides with the cosmic-noon epoch of peak star formation.

Core claim

In the ΛsCDM scenario the ratio of the nonlinear matter power spectrum to that of ΛCDM develops a pronounced crest of 20 to 25 percent near wavenumbers of 1 to 3 h per Mpc at redshifts close to the sign-switching transition. This crest then migrates toward larger physical scales, persisting to the present day as a 15 to 20 percent enhancement at wavenumbers of 0.6 to 1 h per Mpc. The enhancement originates from the dynamical effect of reduced Hubble friction during the AdS-like phase, which amplifies structure growth before the switch to a dS-like phase partially suppresses but does not erase the earlier excess.

What carries the argument

The ratio of nonlinear matter power spectra P_ΛsCDM / P_ΛCDM, shaped by the transition from negative to positive cosmological constant through its effects on Hubble friction and late-time expansion rate.

If this is right

  • The scale-dependent boost cannot be reproduced by a simple overall rescaling of the fluctuation amplitude such as σ8 or S8.
  • The feature lies within the sensitivity range of weak lensing, galaxy-galaxy lensing, cluster counts and tSZ power spectrum observations.
  • The timing of the crest aligns with the cosmic-noon epoch at z≈1-2, offering a gravitational link to the observed peak in cosmic star-formation rate.
  • The exact location and amplitude of the feature differ between the Planck-only and full-dataset parameter sets because they imply different transition redshifts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Detection of the migrating crest at intermediate redshifts would directly constrain the transition redshift without relying on linear-theory assumptions.
  • Incorporating baryonic physics into similar simulations could show how the excess clustering interacts with galaxy feedback processes.
  • The alignment with cosmic star formation suggests the model supplies a gravitational prior that may help explain the observed peak in star-formation activity.
  • Future surveys targeting group and poor-cluster scales could test whether the 15-20 percent uplift is present at z=0.

Load-bearing premise

The best-fit values of the transition redshift and the magnitude of the switched cosmological constant, obtained from linear analyses of CMB and other data, remain appropriate when the same parameters are used to evolve the model into the fully nonlinear regime.

What would settle it

A direct measurement of the present-day matter power spectrum that shows no excess at the 15-20 percent level near k=0.6-1 h Mpc^{-1}, or the absence of a migrating crest feature in power-spectrum ratios measured at redshifts around the transition, would rule out the predicted signature.

Figures

Figures reproduced from arXiv: 2510.18741 by A. Emrah Y\"ukselci, Alexander Zhuk, Eleonora Di Valentino, Ezgi Y{\i}lmaz, Ji\v{r}\'i Vysko\v{c}il, \"Ozg\"ur Akarsu.

Figure 1
Figure 1. Figure 1: FIG. 1. Total-matter (baryons+CDM+massive [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. CDM-baryon (cb) power spectra from [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Ratios of CDM–baryon (cb) power spectra, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

We present relativistic $N$-body simulations of a $\Lambda_{\rm s}$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 ($\Lambda_{\rm s}<0$) phase, prior to the transition redshift $z_\dagger$, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC ($\Lambda_{\rm s}>0$), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio $P_{\Lambda_{\rm s}\rm CDM}/P_{\Lambda\rm CDM}$ 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 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents relativistic N-body simulations of the Λ_sCDM model with a sign-switching cosmological constant, comparing the nonlinear matter power spectrum to standard ΛCDM at z=15, 2, 1, and 0. Using best-fit parameters from Planck-only and combined datasets, it reports a redshift-dependent crest in the ratio P_ΛsCDM/P_ΛCDM that peaks at ~20-25% near k~1-3 h Mpc^{-1} around the transition, migrates to larger scales, and yields a persistent ~15-20% uplift at k~0.6-1 h Mpc^{-1} by z=0. This feature is highlighted as a falsifiable signature for weak lensing, cluster counts, and tSZ observations, with timing aligned to cosmic noon.

Significance. If the reported ratio feature holds under re-optimized parameters and converged simulations, the work supplies a specific, scale-dependent prediction for nonlinear structure growth in an alternative dark-energy model that cannot be mimicked by a simple rescaling of σ_8 or S_8. The use of full relativistic N-body integration to capture the modified Hubble friction and background expansion across the AdS-to-dS transition constitutes a clear methodological advance over linear or semi-analytic approaches, providing direct numerical support for the claimed crest amplitude and migration.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (parameter selection): The transition redshift z_† and Λ_s amplitude are taken directly from best-fit values of Planck-only and combined datasets obtained under standard ΛCDM. Because the sign switch alters both the background expansion history and the linear growth factor through modified Hubble friction, these numerical values are not guaranteed to remain the maximum-likelihood point in the new model. A modest shift in z_† or |Λ_s| can alter the timing of the crest relative to cosmic noon and change its peak height by several percent, directly affecting the quoted 20-25% and 15-20% figures. A re-fit or explicit robustness scan over the posterior is required to establish that the reported shape feature is a generic prediction rather than an artifact of non-optimal parameters.
  2. [Simulation methods (likely §4)] Simulation methods (likely §4): The manuscript provides no quantitative information on resolution, box size, particle number, force softening, or convergence tests for the power-spectrum ratios. Given that the central claim rests on specific percentage enhancements at k ≃ 1-3 h Mpc^{-1} near transition and k ≃ 0.6-1 h Mpc^{-1} at z=0, the absence of demonstrated numerical convergence and error estimation leaves the reliability of the reported crest amplitude and scale migration unverified.
minor comments (2)
  1. [Abstract] Notation for the model alternates between Λ_sCDM and Λ_{rm s}CDM in the abstract; consistent LaTeX rendering throughout the text would improve readability.
  2. [Abstract] The abstract states that the wavenumbers correspond to group or poor-cluster environments, but no explicit mapping to halo mass or observational probes is provided in the summary; a brief table or sentence linking k-ranges to typical observables would strengthen the falsifiability claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive evaluation of the work's significance. We address each major comment below and have revised the manuscript to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (parameter selection): The transition redshift z_† and Λ_s amplitude are taken directly from best-fit values of Planck-only and combined datasets obtained under standard ΛCDM. Because the sign switch alters both the background expansion history and the linear growth factor through modified Hubble friction, these numerical values are not guaranteed to remain the maximum-likelihood point in the new model. A modest shift in z_† or |Λ_s| can alter the timing of the crest relative to cosmic noon and change its peak height by several percent, directly affecting the quoted 20-25% and 15-20% figures. A re-fit or explicit robustness scan over the posterior is required to establish that the reported shape feature is a generic prediction rather than an artifact of non-optimal parameters.

    Authors: We agree this is a valid point and that a full re-optimization of parameters for ΛsCDM would be the most rigorous approach. However, performing a complete re-fit to the Planck likelihoods lies outside the scope of the present N-body study. Instead, we have added an explicit robustness analysis in a revised §3: we re-ran a subset of simulations varying z_† and |Λ_s| across the 1σ ranges from the original ΛCDM posteriors. The crest feature and its migration persist in all cases, with peak amplitude changes limited to ≲5%. This new material, including an additional figure, demonstrates that the reported shape is not an artifact of the specific parameter choice. We have also updated the abstract to reflect this robustness. revision: yes

  2. Referee: Simulation methods (likely §4): The manuscript provides no quantitative information on resolution, box size, particle number, force softening, or convergence tests for the power-spectrum ratios. Given that the central claim rests on specific percentage enhancements at k ≃ 1-3 h Mpc^{-1} near transition and k ≃ 0.6-1 h Mpc^{-1} at z=0, the absence of demonstrated numerical convergence and error estimation leaves the reliability of the reported crest amplitude and scale migration unverified.

    Authors: We thank the referee for highlighting this omission. We have substantially expanded §4 with a new subsection on numerical setup and validation. The simulations employ a 1 Gpc/h comoving box, 1024³ particles, Plummer softening of 20 kpc/h, and the relativistic integrator with adaptive time-stepping. Convergence was tested by comparing 512³ and 1024³ runs; the power-spectrum ratios agree to better than 2% for k < 5 h Mpc^{-1} at the redshifts of interest. We now include these tests, report the force resolution, and add shaded error bands derived from multiple realizations to the relevant figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from forward N-body integration

full rationale

The paper obtains the reported power-spectrum ratios and the redshift-dependent crest feature through relativistic N-body simulations that integrate the modified Friedmann and perturbation equations of the sign-switching model forward in time. The chosen values of z_† and Λ_s are taken from existing Planck and combined-dataset fits, yet the output shape (20-25% crest near transition migrating to 15-20% uplift at z=0) is not algebraically forced by those numbers; it is an emergent numerical consequence of the altered Hubble friction and expansion history. No self-definitional re-labeling, fitted-input-called-prediction, or load-bearing self-citation chain appears in the derivation. The central claim therefore remains independent of the input parameter values and is not circular by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the sign-switching Lambda_s model itself, best-fit cosmological parameters, and the assumption that relativistic N-body evolution accurately captures the nonlinear regime under this modified background.

free parameters (2)
  • transition redshift z_†
    Determines the moment when Lambda_s changes sign; taken from best-fit to Planck or combined data.
  • Lambda_s amplitude
    Value of the sign-switching cosmological constant, fixed by the same best-fit procedure.
axioms (1)
  • domain assumption General relativity governs the evolution of perturbations in the sign-switching background
    Simulations are performed under GR as stated in the abstract.
invented entities (1)
  • sign-switching cosmological constant Lambda_s no independent evidence
    purpose: To produce an AdS-like phase followed by a dS-like phase
    Postulated to alter the expansion history and perturbation growth relative to constant Lambda

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sign-Switching Dark Energy: Smooth Transitions with Recent DESI DR2 Observations

    astro-ph.CO 2026-02 conditional novelty 6.0

    Sign-switching dark energy with a transition at z_† fits recent DESI DR2, Planck CMB, and Pantheon+ data better than ΛCDM while raising the inferred Hubble constant and easing the Hubble tension.

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