{"id":"7da203e0-dd17-428c-9e11-3e8f16390b8b","arxiv_id":"2411.10897","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Relativistic light-cone effects alone generate a nonzero parity-odd galaxy trispectrum, at 10-80% of the even part at large scales.","lead":"This paper calculates a parity-odd part of the galaxy 4-point correlation function (trispectrum) that arises purely from relativistic redshift-space distortions, even when the universe is parity even. It shows the effect can be 10-80% of the even trispectrum at large scales, meaning future parity-violation searches must subtract this contamination.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quantitative claim rests on a truncated relativistic kernel; the full K_GR^(3) is not provided, so the 10–80% amplitudes are not yet reproducible or verified.","rationale":"The reader's weakest_assumption identified exactly this issue: the amplitudes assume all leading-order H/k terms are captured, and Section 4.3 states only dominant terms are shown. As a second-pass stress-tester, I could not find a more load-bearing concern. The central qualitative claim (relativistic effects produce a nonzero parity-odd trispectrum) is well supported by the structure of the kernels: K_GR is odd in mu and thus changes sign under k -> -k, while K_N is even, so the imaginary/odd part is generically nonzero; even an incomplete kernel suffices for existence. The quantitative claim, however, is where the argument is least secure. The paper provides no code and no independent numerical validation, and the K_GR^(3) expression is explicitly labeled as dominant terms only. The lack of a complete kernel is an internal completeness issue, not a matter of disagreeing with prior work, and it directly affects the central quantitative amplitude claim. I therefore agree with the reader's CONDITIONAL verdict and would not change it. I do not endorse REJECT because the qualitative claim and the existence of the effect are compelling and the derivation is standard; the missing pieces are completable.","tokens_in":23121,"tokens_out":1407,"duration_ms":13222,"concrete_test":"Independently derive the full third-order relativistic kernel from Eq. (4.24) using the Fourier conventions in Appendix A, without omitting any terms; then recompute the |Todd/Teven| ratios in Figs. 2–3 at k=0.01 h/Mpc. If the truncated K_GR^(3) in Eq. (4.26) deviates from the full kernel at the 10% level in amplitude, the quantitative claim needs revision; if the deviation is negligible, the concern is resolved.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central quantitative claim is that relativistic projection effects produce an odd-parity trispectrum that is 10% or more (up to 80%) of the even Newtonian trispectrum at equality scales. This claim depends on the completeness of the third-order relativistic kernel K_GR^(3) given in Eq. (4.26). The text explicitly says \"the full expression for the third-order relativistic terms is extremely long and we have given the terms that dominate the relativistic corrections\" (Section 4.3), without stating which terms of Eq. (4.24) were dropped, why they are subdominant, or showing the omitted terms. Section 4.1 also explicitly drops lensing, ISW, gravitational-potential terms, and any (H/k)^2 terms. If any dropped term contributes at the same H/k order with comparable coefficients, the quoted 10–80% ratios change. The qualitative result (nonzero odd trispectrum) is robust, but the headline amplitude is not verifiable from the paper as written. This is an internal-completeness concern, not a disagreement with consensus.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the tree-level galaxy trispectrum in redshift space, including leading relativistic corrections to the observed number counts up to third order in perturbation theory. It separates the trispectrum into parity-even and parity-odd parts under the transformation k_i -> -k_i with a fixed line-of-sight direction, and numerically evaluates the ratio |T_odd/T_even| for Euclid-like and SKA-like survey parameters as a function of configuration angles, viewing angles, scale, folding angle, and redshift. The central quantitative claim is that relativistic projection effects produce a parity-odd trispectrum at the 10% or more level, reaching about 80% in parts of parameter space at k ~ 0.01 h/Mpc.","tokens_in":23471,"tokens_out":13897,"duration_ms":147898,"significance":"If the quantitative claim is correct, the paper identifies an important astrophysical systematic for the recent and future searches for parity violation in the galaxy 4-point function: a parity-odd trispectrum can arise purely from relativistic projection effects even when the underlying density field is parity symmetric. The paper has clear strengths: it correctly identifies the trispectrum as the lowest-order parity-sensitive statistic for a scalar field, assembles the tree-level trispectrum in a standard way, provides explicit first- and second-order kernels and a long third-order GR kernel, and explores a broad parameter space with realistic Euclid- and SKA-like bias parameters using CAMB power spectra. The qualitative conclusion, that a nonzero parity-odd part exists, is robust. However, the headline amplitudes are not fully verifiable from the manuscript as written because the third-order relativistic kernel is presented only through 'dominant' terms, and the treatment of neglected lensing, ISW, and gravitational-potential contributions is not quantified.","major_comments":[{"comment":"The text states: 'The full expression for the third-order relativistic terms is extremely long and we have given the terms that dominate the relativistic corrections.' The manuscript does not specify which terms of Eq. (4.24) are omitted, why they are subdominant, or provide the full expression. Since Eq. (4.26) enters directly into the trispectrum through Eq. (3.10), and since the paper's central claim is the 10-80% amplitude of |T_odd/T_even|, the amplitude claim is not reproducible or checkable from the paper as written. Please provide the complete K_GR^(3), or an explicit list of the dropped terms with scaling estimates, and reconcile this with Appendix C: if Appendix C is intended to be the full kernel, state that explicitly and remove the 'dominant terms' wording.","section":"§4.3, Eq. (4.26)"},{"comment":"Section 4.1 says 'we also neglect the terms that involve gravitational potentials, which are responsible for the effect arising from gravitational redshift... although we leave it for a future analysis.' This is inconsistent with Eq. (4.26), which contains many Omega_m terms originating from the psi couplings in Eq. (4.24) (for example the -9/2 Omega_m bracket), and with Appendix C, which lists these psi terms explicitly. If potential terms are included at third order, the text must say so; if they are meant to be dropped, then those Omega_m terms should be removed and the numerical results recomputed. This matters because the potential terms also carry odd powers of mu and contribute to T_odd.","section":"§4.1 vs §4.3 and Appendix C"},{"comment":"The calculation neglects the integrated lensing-magnification and ISW terms in Eq. (4.7). These are not estimated anywhere, even though they can contribute to parity-odd correlators at comparable order in H/k in some survey configurations, especially at high redshift where magnification bias is non-negligible. Please provide an order-of-magnitude estimate for their contribution to T_odd, or include the dominant integrated terms, or give a quantitative argument for why they are subdominant at the scales and redshifts used for the 10-80% claim.","section":"§4.1 and §5.2"}],"minor_comments":[{"comment":"There are many typographical errors, including 'T rispectrum' in the title, 'bipsectrum', 'signifcantly', 'evergy', and 'asymmetries'; the manuscript needs a careful proofreading pass.","section":"Throughout"},{"comment":"Reference [7] (Cahn, Slepian, Hou 2021) is missing publication details; please add the journal, arXiv identifier, or DOI.","section":"References"},{"comment":"The bias expansion 'delta_g^(3) = b1 delta^(3) + 3b2 delta delta^2 + b3 delta^3' is notationally ambiguous; write the second-order field explicitly as delta^(2) and clarify the factorial/normalization conventions used for b2 and b3.","section":"§4.3, Eq. (4.21)"},{"comment":"The color maps do not have color bars, and the text says the bright yellow regions are where T_even = 0, but the plotted ratio |T_odd/T_even| is then undefined; please add color bars and state how singular regions are treated in the plots.","section":"§5.2, Figs. 2-3"},{"comment":"The bias relation in Eq. (5.9) and the redshift-dependent evolution and magnification bias values should be referenced explicitly to the relevant table in [36].","section":"§5.5"},{"comment":"The numerical results use a single global line-of-sight direction in Eq. (5.2); for the smallest k values shown (k ~ 10^-3 h/Mpc) the combination k r is only of order ten, so the plane-parallel approximation may break down at the same order as the H/k effects being computed. Please state the range of validity of this approximation.","section":"§5.1 and §5.2"},{"comment":"The conclusion refers to the 'monopole of the trispectrum' and its 'dipole' without having defined a multipole decomposition of the trispectrum earlier; please define these terms or rephrase.","section":"§6"}],"recommendation":"major_revision","confidential_remarks":"The qualitative result is persuasive and the topic is well suited to JCAP. The main issue is internal completeness: the third-order GR kernel is explicitly only the 'dominant' part, and the treatment of potential terms is internally inconsistent between Section 4.1 and Section 4.3/Appendix C. These issues are fixable within the scope of the manuscript, so I recommend major revision rather than rejection. The heavy reliance on the authors' own earlier work is appropriate given that they derived the underlying third-order number counts and the companion Letter [27]."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the qualitative result is solid and worth knowing, but the headline amplitudes are not yet reproducible because the third-order relativistic kernel is only given in truncated form.\n\nThe paper is a follow-up to the authors' own PRL, so the central claim—that relativistic projection effects produce an apparent parity-odd galaxy trispectrum—is not new relative to their earlier work. What is new here is the explicit third-order Newtonian and relativistic kernels, the two-survey parameter sweep, and the breakdown of T1113 versus T1122 with their cancellations. The tree-level assembly in Section 3 is standard, and the parity-odd nature of the Doppler-type terms is convincingly argued. The numerical finding that the odd part is 10% or more of the even Newtonian trispectrum at equality scales, reaching 80% for some viewing angles, is a concrete contamination estimate that 4PCF parity searches need.\n\nThe soft spots are internal-completeness issues. Equation (4.26) presents only the \"dominant\" third-order relativistic terms, and the text does not say which terms of (4.24) were dropped or why they are subdominant. There is no code, and no validation against an independent implementation. So the 10–80% amplitudes cannot be checked from the paper as written. The qualitative existence of a nonzero odd part does not depend on those dropped terms, so that part of the argument holds up. The plane-parallel approximation with one global line of sight is another approximation worth flagging, though it likely does not threaten the existence claim. The lack of an SNR forecast is a further gap, but arguably beyond this paper's scope.\n\nSelf-citation is a non-issue here: [27] is their own PRL and this is explicitly the detailed follow-up; the appendices with kernels are the new material. The survey bias parameters come from a standard source.\n\nWho gets value: anyone interpreting BOSS/DESI/Euclid/SKAO parity searches, and anyone modeling relativistic effects in higher-order LSS statistics. I would take the qualitative message seriously and treat the amplitudes as provisional until the full kernel or code appears.\n\nRecommendation: this deserves a serious referee. Send it to review, with the clear conditions: state explicitly which terms are dropped and why, release code or validate against an independent calculation, and add a detection forecast if feasible. I would not desk-reject it.","headline":"Solid follow-up with a robust qualitative claim, but the headline 10–80% amplitudes rest on a truncated third-order kernel and are not yet reproducible from the paper alone.","tokens_in":23864,"tokens_out":2561,"would_cite":true,"duration_ms":28286,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["98.80.-k","98.80.Es"],"model":"deepseek-v4-flash","headline":"Even a parity-symmetric universe produces a parity-odd galaxy trispectrum.","keywords":["trispectrum","parity violation","relativistic projection effects","redshift-space distortions","galaxy number counts","four-point correlation function","tetrahedron configuration","large-scale structure"],"falsifier":"Recompute the trispectrum with the dropped lensing, integrated Sachs–Wolfe, and gravitational-potential terms included, or replace the plane-parallel single-line-of-sight approximation with a wide-angle light-cone computation; if the dropped terms contribute at the same order as the kept Doppler terms, or if wide-angle effects significantly alter the angular dependence, the numerical $10$–$80\\%$ claim fails even though a nonzero odd part survives. A simulation-based test is also decisive: generate a parity-symmetric field, apply the full relativistic mapping, and check whether the measured odd trispectrum matches the predicted dependence on viewing angles.","tokens_in":22895,"feed_emoji":"🔭","tokens_out":12661,"duration_ms":119261,"temperature":0.7,"pith_summary":"This paper argues that a nonzero parity-odd part of the galaxy trispectrum is not evidence for intrinsic parity violation, because relativistic projection effects generate it on their own. The authors compute the observed galaxy number counts to third order in perturbation theory, keeping the leading Doppler-type terms that are suppressed by $H/k$ and odd under $k \\to -k$, and assemble the Fourier-space four-point function (trispectrum) for a tetrahedron of wavevectors. For two representative surveys, at equality scales the odd part is $10\\%$ or more of the even Newtonian trispectrum, rising to $60$–$80\\%$ for some viewing angles. The consequence is that a parity-odd four-point signal is a standard observational artefact of redshift-space galaxy data, and intrinsic-parity claims must survive its subtraction.","feed_headline":"Relativistic effects can mimic parity violation in galaxy surveys","feed_subtitle":"Projection alone adds a 10–80% odd-parity signal to the 4-point correlation function.","key_machinery":"The load-bearing object is the odd-parity trispectrum $T_{\\rm odd} = \\frac{1}{2}[T_g(k_1,k_2,k_3,k_4)-T_g(-k_1,-k_2,-k_3,-k_4)]$, which isolates the imaginary part of the four-point spectrum. The calculation is carried by the relativistic kernels $K_{\\rm GR}^{(1)}, K_{\\rm GR}^{(2)}, K_{\\rm GR}^{(3)}$, which contain only odd powers of $\\mu_i = \\hat{k}_i \\cdot \\hat{n}$ (the cosine between each wavevector and the line of sight), whereas the Newtonian kernels contain only even powers. These odd powers encode the Doppler, evolution-bias, and magnification-bias terms that break symmetry under $k \\to -k$ once a line of sight is fixed. Inserted into the tree-level trispectrum with the tetrahedron geometry parameterized by viewing angles $\\theta,\\phi$ and configuration/folding angles $\\Theta,\\Phi,\\Psi$, they produce the nonzero $T_{\\rm odd}$ that the paper computes.","core_discovery":"The paper's central claim is that even when the underlying matter density field is parity symmetric, the observed galaxy trispectrum in redshift space has a nonzero odd-parity part, because the relativistic corrections to the number counts are not invariant under reversing every wavevector. Working at tree level, the authors split the trispectrum into $T_{\\rm even}$ and $T_{\\rm odd} = \\frac{1}{2}[T_g(k_1,k_2,k_3,k_4)-T_g(-k_1,-k_2,-k_3,-k_4)]$, derive the first-, second-, and third-order Newtonian and relativistic kernels, and evaluate the ratio $|T_{\\rm odd}/T_{\\rm even}|$ numerically over the tetrahedron's configuration and viewing angles. For the two representative surveys (a spectroscopic galaxy survey and a 21cm intensity-mapping survey), the ratio is $10\\%$ or larger at $k \\simeq 0.01\\,h\\,{\\rm Mpc}^{-1}$ and reaches $60$–$80\\%$ for particular viewing angles. The authors conclude that the apparent parity violation in the four-point function is a relativistic projection effect whose size is set by $H/k$ and by the survey's evolution and magnification biases.","pith_inferences":["Because published parity-odd 4PCF detections average over lines of sight, an orientation-resolved measurement would directly separate this relativistic template from any intrinsic signal.","Wide-angle corrections beyond the single-line-of-sight plane-parallel approximation could redistribute the odd signal across multipoles or change the 10–80% amplitudes, an extension the paper leaves for future work.","The same third-order machinery could jointly model the parity-even part of the trispectrum, where relativistic corrections also enter, potentially yielding cleaner constraints on $H/k$ effects and on primordial non-Gaussianity.","A signal-to-noise forecast for upcoming surveys would determine whether the predicted odd part is actually detectable rather than merely present—a step the paper does not take."],"forward_implications":["Any measurement of the galaxy four-point function in redshift space must subtract or model the relativistic odd-parity contribution before an intrinsic parity-violation claim can be made.","At scales near equality ($k \\simeq 0.01\\,h\\,{\\rm Mpc}^{-1}$) the odd part is at least $10\\%$ of the even Newtonian trispectrum, so the effect is not negligible in wide-angle surveys.","The contamination is survey-specific: it depends on the evolution and magnification biases, so different galaxy surveys will see different amplitudes for the same geometry.","Strong cancellations occur between the $T_{1113}$ and $T_{1122}$ contributions, so the total odd signal can be much smaller than the individual terms—relevant for forecasting detectability.","Because the effect grows with $H/k$, it becomes more important at larger scales and higher redshifts, exactly where future surveys gain new sky coverage."],"supporting_citations":[{"why":"the authors' earlier letter establishing apparent parity violation in the observed galaxy trispectrum, which this paper derives in more detail and extends with a parameter scan.","marker":"[27]"},{"why":"provides the third-order relativistic galaxy number counts that are Fourier transformed to build the third-order kernel.","marker":"[19]"},{"why":"introduces the imaginary part of the power spectrum from gravitational redshift, the lineage of the H/k Doppler mechanism used here.","marker":"[20]"},{"why":"computes the parity-odd dipole of the galaxy bispectrum, the three-point analogue that this work generalizes to the trispectrum.","marker":"[25]"},{"why":"derives the parity-odd galaxy bispectrum and gives the even/odd decomposition the authors follow.","marker":"[26]"},{"why":"reports measurements of a parity-odd 4PCF in a spectroscopic galaxy sample, the empirical signal that motivates removing relativistic contaminants.","marker":"[8]"},{"why":"introduces the 4PCF tetrahedron as the lowest-order parity-sensitive statistic in the scalar density field.","marker":"[7]"},{"why":"supplies the evolution and magnification bias parameters used in the two survey examples.","marker":"[36]"},{"why":"computes the matter power spectrum used in the numerical evaluation of the trispectrum.","marker":"[35]"}],"fun_headline_variants":["Relativistic effects mimic parity violation in galaxy surveys","Odd galaxy trispectrum arises from relativity, not intrinsic parity","Relativistic projection adds 10–80% odd signal to 4-point correlation","Even density fields yield odd galaxy trispectrum in redshift space"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The numerical amplitudes assume that the only relativistic corrections that matter are the Doppler-type line-of-sight terms kept in the kernels, with lensing, integrated Sachs–Wolfe, and gravitational-potential terms negligible, and that a single global line of sight is accurate.","fun_headline_variants_meta":{"raw":{"variants":["Relativistic effects mimic parity violation in galaxy surveys","Odd galaxy trispectrum arises from relativity, not intrinsic parity","Relativistic projection adds 10–80% odd signal to 4-point correlation","Even density fields yield odd galaxy trispectrum in redshift space"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000361,"raw_usage":{"total_tokens":1961,"prompt_tokens":969,"completion_tokens":992,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":585,"completion_tokens_details":{"reasoning_tokens":918}},"tokens_in":585,"tokens_out":992,"duration_ms":9655,"temperature":1.0,"reasoning_tokens":918,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:11:00.667884+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the trispectrum with the dropped lensing, integrated Sachs–Wolfe, and gravitational-potential terms included, or replace the plane-parallel single-line-of-sight approximation with a wide-angle light-cone computation; if the dropped terms contribute at the same order as the kept Doppler terms, or if wide-angle effects significantly alter the angular dependence, the numerical $10$–$80\\%$ claim fails even though a nonzero odd part survives. A simulation-based test is also decisive: generate a parity-symmetric field, apply the full relativistic mapping, and check whether the measured odd trispectrum matches the predicted dependence on viewing angles.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the authors' earlier letter establishing apparent parity violation in the observed galaxy trispectrum, which this paper derives in more detail and extends with a parameter scan."},{"cited_title":"Dio and U","cited_arxiv_id":null,"evidence_quote":"provides the third-order relativistic galaxy number counts that are Fourier transformed to build the third-order kernel."},{"cited_title":"McDonald,Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum, Journal of Cosmology and Astroparticle Physics2009 (2009) 026–026","cited_arxiv_id":null,"evidence_quote":"introduces the imaginary part of the power spectrum from gravitational redshift, the lineage of the H/k Doppler mechanism used here."},{"cited_title":"Jeong and F","cited_arxiv_id":null,"evidence_quote":"derives the parity-odd galaxy bispectrum and gives the even/odd decomposition the authors follow."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reports measurements of a parity-odd 4PCF in a spectroscopic galaxy sample, the empirical signal that motivates removing relativistic contaminants."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"introduces the 4PCF tetrahedron as the lowest-order parity-sensitive statistic in the scalar density field."},{"cited_title":"Maartens, J","cited_arxiv_id":null,"evidence_quote":"supplies the evolution and magnification bias parameters used in the two survey examples."},{"cited_title":"Lewis, A","cited_arxiv_id":null,"evidence_quote":"computes the matter power spectrum used in the numerical evaluation of the trispectrum."}],"review_version":1}