{"id":"c373adec-33bb-45f9-ae62-609e6b010baa","arxiv_id":"1908.05683","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Full Einstein-Vlasov simulations show Newtonian N-body collapse is faster than general relativity for extreme density perturbations, but accurate at subpercent level for standard cosmological amplitudes.","lead":"This paper uses full general-relativistic Einstein-Vlasov simulations to follow cosmic structure formation, including the formation of bound halos, and compares them to standard Newtonian N-body simulations. For large-amplitude perturbations the Newtonian collapse is faster, while for standard cosmological amplitudes the two agree at the subpercent level, supporting the use of Newtonian codes for large-scale structure and cosmic variance.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Single-mode super-LCDM initial conditions do not establish that GR corrections to cosmic-variance H0 estimates are negligible for realistic multi-scale density fields.","rationale":"The reader's verdict is ACCEPT and identifies the idealized single-scale initial conditions as the weakest assumption; I agree that this is the load-bearing concern. However, I would move the verdict to CONDITIONAL because the paper's most impactful conclusion—that GR corrections to cosmic variance in H0 are negligible—requires more than an extrapolation in amplitude. The simulations provide credible, converged support for the core numerical comparison, and the paper honestly acknowledges the single-wavelength limitation. But the transition from 'subpercent DL(z) differences in a single-mode spacetime' to 'negligible GR corrections to cosmic variance' is an extrapolation in the structure of the density field, not just in amplitude. A realistic density field has many modes, nonlinear mode coupling, and statistical averaging over the Hubble volume, none of which are tested here. Without a specific multi-mode check or a conditioning of the conclusion, the broad H0 claim is stronger than the evidence supports. Hence CONDITIONAL rather than UNCHANGED: accept the numerical comparison, but require the cosmic-variance conclusion to be either qualified or tested against a more realistic spectrum.","tokens_in":12668,"tokens_out":10644,"duration_ms":114728,"concrete_test":"Re-run the Einstein-Vlasov and matched GADGET-2 simulations in the same domain with initial density contrast built from a superposition of the first four LCDM linear-power-spectrum modes (k/k_H = 0.5, 1, 2, 4, random phases, amplitudes normalized to sigma_8), and compare (i) the maximum fractional GR-Newtonian difference in DL(z) over the same set of fiducial null rays and (ii) the fractional GR-Newtonian difference in the local expansion scalar averaged over fiducial observers. If either exceeds roughly 0.5%—the quoted cosmic-variance budget—or if the first-crossing-time offset deviates from the single-mode trend by more than 10%, the single-mode setup is not a sufficient proxy and the H0-variance conclusion is unsupported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section IV concludes that 'GR corrections to the Newtonian calculation of the cosmic variance in the local measurement of the Hubble constant are negligible.' This rests on simulations (Sec. II.A, Eq. 1) with a single sinusoidal density perturbation per Cartesian axis at wavelength 4/H0, with no power spectrum and no modes below that scale. For standard-amplitude runs the measured GR-Newtonian differences in DL(z) are subpercent (Fig. 4), but the quantity actually bounded is not cosmic variance: it is the difference along a small set of null rays in a specially symmetric, single-mode spacetime. Cosmic variance in H0 is an ensemble property of a statistically homogeneous Gaussian random field, where many modes at different wavelengths contribute and nonlinear small-scale structures could backreact differently. The paper provides no argument or calculation that the single-mode configuration bounds the multi-mode case; it simply asserts the leap. This is an external-validity gap in the strongest claim, not an internal inconsistency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper performs fully general-relativistic Einstein-Vlasov (collisionless N-body) simulations of structure formation and compares them with standard Newtonian N-body simulations (GADGET-2) on matched initial conditions. The initial conditions are sinusoidal density perturbations along each Cartesian axis at a single wavelength, with amplitudes ranging from near-LCDM values up to extreme super-LCDM cases. The authors compare density contrasts at maxima and minima, infall trajectories of fiducial particles, and luminosity distance--redshift relations along null geodesics. They find that for small amplitudes the Newtonian and GR calculations agree at the subpercent level, while for large amplitudes the Newtonian collapse occurs faster, with differences concentrated near regions of large gravitational potential and relativistic infall velocities. The paper concludes that Newtonian N-body simulations are strongly validated for standard cosmological structures and that GR corrections to the cosmic variance in the local Hubble constant are negligible.","tokens_in":12800,"tokens_out":4201,"duration_ms":47974,"significance":"If the results hold, this is a valuable step beyond earlier fluid-based GR structure-formation simulations, because the Einstein-Vlasov treatment remains valid through multistreaming and halo formation. The methodology is careful: there are no free parameters fitted to the results; the Newtonian reference uses the public, well-tested GADGET-2 code; the GR code has been independently applied to black-hole formation; and the appendix reports convergence tests for constraints, crossing times, and luminosity distances. The main limitation is external validity: the idealized single-wavelength initial conditions do not automatically bound the multi-scale, statistically homogeneous density fields relevant to cosmic-variance claims. This gap affects the strongest concluding statements but is fixable by more cautious wording or an additional argument.","major_comments":[{"comment":"The concluding claim that GR corrections to the Newtonian calculation of cosmic variance in the local Hubble constant are negligible is not supported by the evidence presented. The simulations (Eq. (1)) begin with a single sinusoidal density perturbation per Cartesian axis, with no power spectrum and no modes below the initial wavelength. Cosmic variance in H0 is an ensemble property of a multi-mode, statistically homogeneous density field, and the paper does not provide an argument that the single-mode configuration bounds the multi-mode case. In fact, the paper itself states that tackling a more realistic power spectrum will require adaptive mesh refinement and further work. This is a load-bearing external-validity gap: the abstract's 'standard cosmological values' conclusion rests on it. I recommend either softening the conclusion to the configurations studied or adding a quantitative argument (e.g., mode-coupling/backreaction estimates) connecting the single-mode results to realistic spectra.","section":"Section IV and Abstract"},{"comment":"The quantity actually computed is the fractional difference in DL(z) along a small set of null rays between the maximum and minimum density points, not an estimator of the cosmic variance in a local H0 measurement. The inference from subpercent differences in these DL(z) curves to 'negligible' GR corrections to H0 cosmic variance involves an additional assumption: that these rays and this symmetric configuration are representative of the averaging volume and observer selection relevant to local H0 measurements. No direct computation of an H0 estimator in both frameworks is given. Since this is presented as a strengthening of the Hubble-constant tension discussion, the link should either be made explicit or the conclusion should be restricted to the observables actually simulated.","section":"Section IV and Fig. 4"}],"minor_comments":[{"comment":"The second author's name appears as 'Rados/suppress law Wojtak'; this is clearly a corruption and should be corrected to the proper spelling.","section":"Author list / title page"},{"comment":"The left-column label 'D_L/D_LFRW L - 1' is garbled and should be rewritten, for example as 'D_L/D_LFRW - 1'.","section":"Fig. 4 caption"},{"comment":"The description of the GR initial conditions says particle positions are obtained 'by starting from a uniform lattice ... and then displacing each particle slightly according to the Zel'dovich approximation' with a reference to Eq. (31) of Ref. [24], but the precise relation to the Newtonian dictionary and the mass-rescaling correction is only sketched. A reader would benefit from one or two more equations showing how the GR density and metric are fixed.","section":"Section II.C"},{"comment":"The resolution comparison uses different particle numbers for the GR and Newtonian runs at each 'resolution' (e.g., GR N=192^3 vs Newtonian N=128^3 at low resolution), which complicates the interpretation of the plotted differences; the text should state whether this mismatch is deliberate and how it affects the truncation-error estimate.","section":"Appendix, Fig. 8"},{"comment":"The abbreviations 'Newt. UD->OD', 'GR UD->OD', etc. are not defined in the captions; they should be spelled out at first use.","section":"Figure labels throughout"}],"recommendation":"major_revision","confidential_remarks":"This is a solid and interesting paper that is close to acceptance. My main reservation is the leap from idealized single-mode initial conditions to the strong statement about cosmic variance in the local Hubble constant. That statement appears in the abstract and conclusion, so it is not a purely cosmetic overstatement; it either needs to be supported by an additional argument or calculation, or the wording needs to be scaled back to what the simulations actually show. If the authors are willing to make that change, I would expect the revised version to be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is the first Einstein-Vlasov cosmological structure-formation calculation that carries the Newtonian-vs-GR comparison through shell crossing, and it largely supports the standard Newtonian treatment for cosmologically relevant amplitudes. The main weakness is that the strongest concluding remark about cosmic variance in H0 goes beyond what the single-mode initial conditions can show.\n\nWhat's new: East, Wojtak, and Pretorius extend their earlier fluid-based comparison (Ref. [7]) to collisionless matter using the Einstein-Vlasov code from Pretorius & East. That lets them follow halo formation, shell crossing, and multistreaming in the fully GR spacetime, which fluid treatments cannot do. They match Newtonian GADGET-2 simulations to the GR runs through the Chisari-Zaldarriaga/Green-Wald dictionary, and they check convergence of constraints, halo crossing times, and D_L(z) in the appendix. No free parameters are fit. The central finding—Newtonian collapse proceeds slightly faster, with subpercent agreement in D_L(z) for |ΨN| below roughly 0.1—is credible and cleanly presented. The extreme δ = 0.05 case, where Newtonian gravity breaks down, is also handled honestly.\n\nThe soft spot is the inference to cosmic variance. The simulations use a single sinusoidal perturbation per axis at wavelength 4/H0; there is no power spectrum, no mode coupling from smaller-scale nonlinearities, and the GR runs use uniform grids rather than AMR. Figure 4's right column bounds the GR-Newtonian difference along a small set of null rays in that symmetric setup. To conclude from this that GR corrections to the ensemble-level cosmic variance in H0 are negligible is a leap. The authors hedge by saying \"corroborate\" and they cite Macpherson et al. for a power-spectrum calculation, but the sentence in Sec. IV that \"our comparison implies\" negligible GR corrections is stronger than the evidence presented. This is an external-validity gap, not an internal inconsistency. The authors acknowledge the single-scale limitation and the need for AMR, so they are not hiding it.\n\nAlso note: no code or data release, so independent reproduction from the manuscript alone is not possible. That is a recurring issue in the field but still worth flagging.\n\nWho this is for: cosmologists who run N-body simulations and want a quantitative handle on relativistic corrections, plus GR numerics people interested in Einstein-Vlasov methods. The paper deserves serious refereeing and publication; the core comparison is careful and the main claims hold. I would recommend acceptance with a revision that either softens the cosmic-variance sentence or provides an explicit argument for why the single-mode result bounds the multi-mode case.","headline":"First Einstein-Vlasov structure-formation runs through halo formation; solid Newtonian/GR comparison, but the H0 cosmic-variance conclusion overreaches the single-mode setup.","tokens_in":13320,"tokens_out":2407,"would_cite":true,"duration_ms":25067,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Full general-relativistic N-body calculations show Newtonian gravity accurately predicts structure formation for cosmological perturbations, diverging only at relativistic extremes.","keywords":["Einstein-Vlasov equations","Newtonian N-body simulations","structure formation","general relativity","cosmic variance","Hubble constant tension","backreaction","luminosity distance"],"falsifier":"Run a matched pair of Newtonian and Einstein-Vlasov simulations with a realistic $\\Lambda$CDM power spectrum on Gpc scales, using adaptive mesh refinement around the first collapsed halos, and compare halo collapse times and $D_L(z)$ in regions where the Newtonian potential is below $|\\psi|=0.1$; if the differences there exceed the subpercent level found here, the paper's central conclusion fails.","tokens_in":1521,"feed_emoji":"🌌","tokens_out":2712,"duration_ms":84819,"temperature":0.7,"pith_summary":"This paper tests the standard tool of cosmological structure formation, Newtonian N-body simulations, against full solutions of the Einstein-Vlasov equations, which treat dark matter as collisionless particles coupled to general relativity. Using simplified single-wavelength density perturbations scaled from small to extreme amplitudes, it finds that the two descriptions agree to subpercent accuracy for perturbations of cosmological size, all the way into the nonlinear regime where halos form. At amplitudes far beyond standard cosmology, the Newtonian runs collapse overdense regions faster than the fully relativistic runs, and the gap widens as the gravitational potential approaches unity; even then, the expansion and light propagation outside the strong-field regions stay close between the two methods. The result matters because it validates the Newtonian basis of large-scale structure predictions and implies that general-relativistic corrections to the local measurement of the Hubble constant, through cosmic variance, are negligible.","feed_headline":"Newtonian gravity survives a full general-relativistic N-body test","feed_subtitle":"Newtonian and full Einstein-Vlasov runs agree to subpercent accuracy at cosmological amplitudes.","key_machinery":"The central machinery is the Einstein-Vlasov system, collisionless matter particles moving on a dynamically evolved spacetime, as the fully relativistic counterpart to Newtonian N-body gravity. The comparison is carried by a Newtonian-to-GR dictionary that maps the same Zel'dovich initial displacements into constraint-satisfying relativistic initial data, and by observables defined with respect to fiducial observers: the density contrast as a function of proper time and the luminosity-distance-versus-redshift relation of null geodesics. This lets the two simulations be compared in a way that avoids coordinate artifacts and continues past shell crossing, which is where fluid treatments break down.","core_discovery":"On the paper's own terms, the discovery is a quantitative, gauge-aware comparison: for initial density contrasts $\\bar\\delta\\times 10^2=0.25$, $0.5$, $1$, and $5$ with a wavelength four times the initial Hubble radius, the Newtonian and Einstein-Vlasov evolutions produce nearly identical density contrasts along fiducial observers and nearly identical distance-redshift relations, with differences typically below about one percent and consistent with truncation error, as long as the Newtonian potential stays below $|\\psi|\\sim 0.1$. When the inhomogeneity is pushed to the extreme limit, collapse at the overdensity occurs earlier in Newtonian gravity and infall velocities become relativistic, while the fully relativistic solution continues toward black hole formation; nevertheless, the void region and the global expansion remain close. The paper claims that this bounds relativistic backreaction and validates standard Newtonian N-body methods for observations at cosmological scales, including estimates of cosmic variance in $H_0$.","pith_inferences":["If the single-wavelength idealization hides mode coupling, a realistic-spectrum Einstein-Vlasov run could reveal general-relativistic corrections larger than subpercent on small scales; the paper's conclusion is therefore conditional on the shape of the power spectrum.","The delay of collapse in full general relativity suggests an effective relativistic slowdown of infall that may matter for primordial black hole formation in a matter-dominated era, where densities reach the extreme amplitudes studied here.","The same fiducial-observer comparison could be extended to redshift-space distortions or weak lensing, where subpercent relativistic corrections may become observable with next-generation surveys.","A realistic-spectrum extension would also test whether the near-identical void evolution seen here persists when the void is surrounded by many nonlinear halos rather than a single sinusoidal perturbation."],"forward_implications":["Newtonian N-body simulations are validated for large-scale perturbations at standard cosmological amplitudes, with general-relativistic corrections below about one percent.","General-relativistic corrections to cosmic variance in the local Hubble constant are negligible, so the roughly nine percent tension between local and CMB-based $H_0$ measurements cannot be explained by cosmic variance.","In the strong-field regime, full general relativity slows the collapse of overdense regions relative to Newtonian gravity, with the discrepancy growing as potentials approach unity.","Outside the high-density, high-velocity regions, void evolution and light propagation remain close between the two methods, bounding the possible backreaction of nonlinear structures on the global expansion.","Treating matter as particles in the Einstein-Vlasov framework allows the comparison to continue through multistream regions, where pressureless fluid descriptions break down."],"supporting_citations":[{"why":"Defines the Newtonian-GR comparison dictionary and the fluid-based baseline that this paper extends beyond shell crossing.","marker":"[7]"},{"why":"Supplies the Einstein-Vlasov evolution method that permits an N-body comparison in multistream regions.","marker":"[23]"},{"why":"Provides the dictionary relating Newtonian and GR variables used to build consistent initial conditions.","marker":"[24]"},{"why":"Provides the GR correspondence for the Newtonian spacetime used in constructing initial data and interpreting observables.","marker":"[25]"},{"why":"Gives the Zel'dovich approximation used to set the initial particle displacements in both simulations.","marker":"[26]"},{"why":"Supplies the Lagrangian tessellation density estimator used for the Newtonian density field in single-stream and multistream regions.","marker":"[33]"},{"why":"Supplies the tetrahedral density-estimation technique the Newtonian comparison relies on and calibrates its resolution limits.","marker":"[34]"},{"why":"Provides the Newtonian estimate of cosmic variance in the local Hubble constant whose negligible size the paper corroborates from full general relativity.","marker":"[39]"},{"why":"Provides a recent general-relativistic fluid calculation with a cosmological power spectrum that independently reached the same conclusion about local expansion variations.","marker":"[42]"}],"fun_headline_variants":["Einstein-Vlasov vs Newton: subpercent agreement on cosmic scales","Relativistic N-body check: Newtonian holds up to AI","GR vs Newton: cosmic structure formation agrees to ~1%","Full GR N-body validates Newtonian simulations at large scales","Newtonian and Einstein-Vlasov match for cosmological perturbations"],"cache_read_input_tokens":15616,"weakest_assumption_plain":"The broad conclusions assume that a single-wavelength sinusoidal perturbation, rather than a realistic spectrum of fluctuations, captures the relativistic corrections that matter in real cosmology; if mode coupling or small-scale nonlinearities change those corrections, the validation of Newtonian simulations would not automatically extend.","fun_headline_variants_meta":{"raw":{"variants":["Einstein-Vlasov vs Newton: subpercent agreement on cosmic scales","Relativistic N-body check: Newtonian holds up to AI","GR vs Newton: cosmic structure formation agrees to ~1%","Full GR N-body validates Newtonian simulations at large scales","Newtonian and Einstein-Vlasov match for cosmological perturbations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000158,"raw_usage":{"total_tokens":1205,"prompt_tokens":908,"completion_tokens":297,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":524,"completion_tokens_details":{"reasoning_tokens":210}},"tokens_in":524,"tokens_out":297,"duration_ms":3399,"temperature":1.0,"reasoning_tokens":210,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:07:30.399812+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a matched pair of Newtonian and Einstein-Vlasov simulations with a realistic $\\Lambda$CDM power spectrum on Gpc scales, using adaptive mesh refinement around the first collapsed halos, and compare halo collapse times and $D_L(z)$ in regions where the Newtonian potential is below $|\\psi|=0.1$; if the differences there exceed the subpercent level found here, the paper's central conclusion fails.","supporting_citations":[{"cited_title":"Robustness of Cosmological Simulations I: Large Scale Structure","cited_arxiv_id":"astro-ph/0411795","evidence_quote":"Supplies the tetrahedral density-estimation technique the Newtonian comparison relies on and calibrates its resolution limits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Newtonian estimate of cosmic variance in the local Hubble constant whose negligible size the paper corroborates from full general relativity."}],"review_version":1}