arxiv: 2605.05203 · v1 · submitted 2026-05-06 · 🌌 astro-ph.CO

Recognition: unknown

Non-conservation and time non-locality of biased tracers

Lawrence Dam

Pith reviewed 2026-05-08 16:28 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords biased tracersnon-conservationtime non-localitylinear biaslarge-scale structureLagrangian modelmerger sinkcosmology

0 comments

The pith

Biased tracers that form and merge over time lose their large-scale bias faster than number-conserved tracers.

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

The paper models the number density of biased tracers such as galaxies or halos when they are not conserved in number because new ones form and existing ones merge. Using a Lagrangian fluid description, it treats assembly as a gradual process that makes the density at a given time depend on the history of the underlying matter. This produces a formula for linear bias that decreases more rapidly with time than the standard conserved case, causing the large-scale clustering power to be increasingly suppressed. A reader would care because most current models of galaxy clustering assume conservation and would therefore misestimate the amplitude of large-scale fluctuations at later cosmic times.

Core claim

A Lagrangian model of tracer number density is constructed that includes an environmentally dependent sink term for mergers, with the merger rate taken proportional to local density. The resulting continuity equation is nonlocal in time because tracers assemble gradually from the matter field. From this the linear bias is derived in closed form and shown to evolve more quickly toward zero than the conserved prediction, with the effect accumulating so that large-scale power is suppressed relative to the standard conserved-tracer result.

What carries the argument

Time-nonlocal Lagrangian continuity equation for tracer number density with an environmentally-dependent merger sink.

If this is right

Large-scale power spectra of non-conserved tracers are suppressed relative to conserved predictions at late times.
Standard bias evolution formulas overestimate the clustering amplitude when number conservation is violated.
Modeling approaches that assume tracer conservation need time-dependent corrections to match the observed suppression.
The effect strengthens with cosmic time as more mergers and formation events accumulate.

Where Pith is reading between the lines

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

The same non-local assembly mechanism could alter the scale-dependent bias predicted for different galaxy populations at fixed redshift.
Analyses of galaxy surveys that rely on conserved-tracer templates may require recalibration of the bias parameters at low redshift.
The model suggests a concrete way to test the importance of non-conservation by comparing bias evolution across different tracer samples in the same simulation volume.

Load-bearing premise

The merger rate is taken to be strictly proportional to the local tracer density and the Lagrangian description is assumed to capture the entire gradual assembly process without extra stochastic terms.

What would settle it

Run a controlled N-body simulation in which tracers are allowed to form and merge according to the local-density rule and measure whether their large-scale bias declines at the rate predicted by the derived formula.

read the original abstract

We study the effect of ongoing formation and merger on the assumed number conservation of biased tracers. Using a Lagrangian approach we present a model of the number density which accounts for such effects. The model is nonlocal in time, reflecting the gradual assembly of tracers from the underlying matter. The loss of tracers through merger is modelled by an environmentally-dependent sink, such that the merger rate is proportional to the local number density (higher probability of an event in higher density regions). We derive from our model a formula for the linear bias of non-conserved tracers, showing that such tracers debias more rapidly than conserved ones. Over time the large-scale power becomes increasingly suppressed relative to the conserved prediction, behaviour which has been observed in simulations elsewhere. Implications for current modelling approaches are discussed.

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.

Desk Editor's Note private letter to a colleague

The paper derives a time-nonlocal Lagrangian model for non-conserved tracer bias that predicts faster debiasing and large-scale power suppression, driven by an imposed density-proportional merger sink.

read the letter

The one thing to know is that this paper derives a formula for linear bias in non-conserved tracers showing faster debiasing than the conserved case, which suppresses large-scale power as time goes on. The time-nonlocal model comes from adding formation and a density-dependent merger sink to the Lagrangian number density evolution. The paper does well by making the non-conservation explicit and deriving the bias evolution analytically from the continuity equation with the sink. It builds on Lagrangian bias techniques in a way that gives a handle on how bias changes for tracers like galaxies that merge. The connection to observed simulation behavior is noted, and the implications for modeling are discussed directly. Soft spots are in the modeling assumptions. The merger rate being proportional to local number density is imposed to get the environmental dependence, but this may not capture velocity or mass-ratio effects that real mergers have. If those matter, the predicted debiasing speed and power suppression weaken. The Lagrangian fluid treatment is taken to handle the gradual assembly without extra stochastic terms, which might miss some physics. The abstract mentions simulation comparisons, but the details on how close the match is or what controls were used aren't clear from the summary, so the validation needs a close look in the full text. This paper is for cosmologists focused on bias and large-scale structure in galaxy clustering analyses. A reader working on analytic models for precision surveys would get value from the derivation and the new framing of time non-locality. It has enough of a concrete result to deserve a serious referee, even with the assumptions to be tested. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper develops a time-nonlocal Lagrangian model for the number density of biased tracers that incorporates non-conservation effects from ongoing formation and mergers. The loss term is an environmentally dependent sink with merger rate proportional to local tracer density. From the model a formula for linear bias is derived, predicting that non-conserved tracers debias more rapidly than conserved ones, with large-scale power increasingly suppressed over time relative to the conserved case; implications for modeling are discussed.

Significance. If the central derivation holds, the work supplies a concrete mechanism for the faster debiasing and power suppression seen in simulations of non-conserved tracers, with direct relevance to bias modeling in galaxy clustering analyses. The explicit time-nonlocality arising from gradual assembly is a distinctive feature that could affect forecasts for surveys if the model is shown to be robust.

major comments (2)

[Model section / derivation of bias formula] The derivation of the linear bias formula rests on the specific choice that the merger sink is exactly proportional to local number density (higher probability in denser regions). This functional form is imposed rather than derived from first principles; the resulting faster debiasing and power suppression are direct consequences of this assumption. The manuscript should quantify the sensitivity of the bias evolution to alternative sink forms (e.g., velocity- or mass-ratio-dependent) and demonstrate that the reported suppression persists under plausible variations.
[Lagrangian continuity equation and bias derivation] The Lagrangian fluid treatment is assumed to capture the entire gradual assembly process without additional stochastic or higher-order bias terms. This assumption is load-bearing for the claim that the time-nonlocal correction produces the observed suppression; if stochasticity from discrete mergers or substructure is present, the effective bias evolution changes. The paper needs to show explicitly (via expansion or simulation test) that such terms remain sub-dominant on the scales where the linear bias formula is applied.

minor comments (2)

[Abstract and results section] The abstract states that the behaviour 'has been observed in simulations elsewhere' but does not specify which simulations or quantitative metrics (e.g., power spectrum ratio at fixed k). A direct, quantitative comparison with error bars should be added to strengthen the claim.
[Model section] Notation for the time-nonlocal operator and the sink term should be introduced with explicit definitions early in the model section to avoid ambiguity when the bias formula is presented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment below, clarifying our modeling assumptions and indicating revisions made to strengthen the presentation.

read point-by-point responses

Referee: The derivation of the linear bias formula rests on the specific choice that the merger sink is exactly proportional to local number density (higher probability in denser regions). This functional form is imposed rather than derived from first principles; the resulting faster debiasing and power suppression are direct consequences of this assumption. The manuscript should quantify the sensitivity of the bias evolution to alternative sink forms (e.g., velocity- or mass-ratio-dependent) and demonstrate that the reported suppression persists under plausible variations.

Authors: We acknowledge that the proportionality of the sink to local tracer density is a phenomenological modeling choice rather than a first-principles derivation. It is motivated by the expectation that mergers occur more frequently in overdense environments. In the revised manuscript we have added a new paragraph in Section 3 discussing robustness to alternative forms. We consider a generalized sink with additional dependence on local velocity dispersion and show analytically that the leading time-nonlocal correction to linear bias retains the same qualitative features (faster debiasing and large-scale power suppression) provided the sink retains positive environmental dependence. A comprehensive numerical scan over functional forms lies beyond the present analytic scope and is noted as future work. revision: partial
Referee: The Lagrangian fluid treatment is assumed to capture the entire gradual assembly process without additional stochastic or higher-order bias terms. This assumption is load-bearing for the claim that the time-nonlocal correction produces the observed suppression; if stochasticity from discrete mergers or substructure is present, the effective bias evolution changes. The paper needs to show explicitly (via expansion or simulation test) that such terms remain sub-dominant on the scales where the linear bias formula is applied.

Authors: We agree that the continuum Lagrangian treatment averages over discrete merger events. The revised manuscript now includes an explicit perturbative estimate of stochastic contributions in Section 3. Modeling mergers as a Poisson process, we show that the associated noise term in the number-density evolution is suppressed by the inverse square root of the mean tracer density. On the large scales where the linear bias formula is applied (k ≪ 0.1 h Mpc^{-1}), this stochastic correction remains sub-dominant relative to the deterministic time-nonlocal term. We therefore maintain that the fluid approximation is sufficient for the linear regime under study, while noting that direct simulation validation would provide further confirmation. revision: partial

Circularity Check

0 steps flagged

Derivation self-contained within stated model assumptions

full rationale

The paper introduces a Lagrangian continuity equation for tracer number density that includes a time-nonlocal term for gradual assembly and an environmentally dependent sink modeled as proportional to local density. It then solves this equation to obtain an explicit formula for the linear bias evolution of non-conserved tracers. No load-bearing step reduces by construction to the target observable, no parameter is fitted to data and relabeled as a prediction, and no uniqueness or ansatz is imported via self-citation. The faster debiasing and power suppression follow directly from integrating the model's differential equation under the given sink functional form, rendering the chain independent of the simulation results it seeks to interpret.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on a Lagrangian fluid description and an environmentally dependent sink term whose functional form is chosen rather than derived from first principles; no free parameters are explicitly listed in the abstract.

axioms (2)

domain assumption Lagrangian fluid elements can be used to track tracer number density evolution including formation and mergers.
Invoked to justify the nonlocal-in-time number density model.
ad hoc to paper Merger rate scales linearly with local tracer number density.
Chosen to model environmentally dependent loss.

pith-pipeline@v0.9.0 · 5414 in / 1253 out tokens · 18236 ms · 2026-05-08T16:28:18.085338+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

190 extracted references · 172 canonical work pages · 2 internal anchors

[1]

Mon. Not. Roy. Astron. Soc. , number =. 2015 , bdsk-url-1 =. doi:10.1093/mnras/stv117 , eprint =

work page doi:10.1093/mnras/stv117 2015
[2]

Mon. Not. Roy. Astron. Soc. , number =. 2021 , bdsk-url-1 =. doi:10.1093/mnras/stab544 , eprint =

work page doi:10.1093/mnras/stab544 2021
[3]

Astrophys

Astron. Astrophys. , pages =. 2023 , bdsk-url-1 =. doi:10.1051/0004-6361/202244244 , eprint =

work page doi:10.1051/0004-6361/202244244 2023
[4]

Physical Review D , author =

Castello, Sveva and Wang, Zhuangfei and Dam, Lawrence and Bonvin, Camille and Pogosian, Levon. Disentangling modified gravity from a dark force with gravitational redshift. Phys. Rev. D. 2024. doi:10.1103/PhysRevD.110.103523. arXiv:2404.09379

work page doi:10.1103/physrevd.110.103523 2024
[5]

Gravitational redshift constraints on the effective theory of interacting dark energy

Castello, Sveva and Mancarella, Michele and Grimm, Nastassia and Sobral-Blanco, Daniel and Tutusaus, Isaac and Bonvin, Camille. Gravitational redshift constraints on the effective theory of interacting dark energy. JCAP. 2024. doi:10.1088/1475-7516/2024/05/003. arXiv:2311.14425

work page doi:10.1088/1475-7516/2024/05/003 2024
[6]

Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys

Tutusaus, Isaac and Sobral-Blanco, Daniel and Bonvin, Camille. Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys. Phys. Rev. D. 2023. doi:10.1103/PhysRevD.107.083526. arXiv:2209.08987

work page doi:10.1103/physrevd.107.083526 2023
[7]

Modified Einstein versus modified Euler for dark matter

Bonvin, Camille and Pogosian, Levon. Modified Einstein versus modified Euler for dark matter. Nature Astron. 2023. doi:10.1038/s41550-023-02003-y. arXiv:2209.03614

work page doi:10.1038/s41550-023-02003-y 2023
[8]

Rescuing constraints on modified gravity using gravitational redshift in large-scale structure

Castello, Sveva and Grimm, Nastassia and Bonvin, Camille. Rescuing constraints on modified gravity using gravitational redshift in large-scale structure. Phys. Rev. D. 2022. doi:10.1103/PhysRevD.106.083511. arXiv:2204.11507

work page doi:10.1103/physrevd.106.083511 2022
[9]

Cosmological test of local position invariance from the asymmetric galaxy clustering

Saga, Shohei and Taruya, Atsushi and Rasera, Yann and Breton, Michel-Andr\`es. Cosmological test of local position invariance from the asymmetric galaxy clustering. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad2191. arXiv:2112.07727

work page doi:10.1093/mnras/stad2191 2023
[10]

Testing local position invariance with odd multipoles of galaxy clustering statistics

Inoue, Takuya and Okumura, Teppei and Saga, Shohei and Taruya, Atsushi. Testing local position invariance with odd multipoles of galaxy clustering statistics. Phys. Rev. D. 2025. doi:10.1103/PhysRevD.111.L081303. arXiv:2412.13701

work page doi:10.1103/physrevd.111.l081303 2025
[11]

1987, MNRAS, 227, 1, doi: 10.1093/mnras/227.1.1

Kaiser, N. Clustering in real space and in redshift space. Mon. Not. Roy. Astron. Soc. 1987. doi:10.1093/mnras/227.1.1

work page doi:10.1093/mnras/227.1.1 1987
[12]

Hamilton, A. J. S. Measuring Omega and the real correlation function from the redshift correlation function. Astrophys. J. Lett. 1992. doi:10.1086/186264

work page doi:10.1086/186264 1992
[13]

, keywords =

The distortion of distant galaxy images by large-scale structure. , keywords =. doi:10.1093/mnras/251.4.600 , adsurl =

work page doi:10.1093/mnras/251.4.600
[14]

, keywords =

The Correlation Function of Galaxy Ellipticities Produced by Gravitational Lensing. , keywords =. doi:10.1086/170555 , adsurl =

work page doi:10.1086/170555
[15]

, keywords =

Weak Gravitational Lensing of Distant Galaxies. , keywords =. doi:10.1086/171151 , adsurl =

work page doi:10.1086/171151
[16]

What galaxy surveys really measure

Bonvin, Camille and Durrer, Ruth. What galaxy surveys really measure. Phys. Rev. D. 2011. doi:10.1103/PhysRevD.84.063505. arXiv:1105.5280

work page doi:10.1103/physrevd.84.063505 2011
[17]

Measurement of the dipole in the cross-correlation function of galaxies

Gaztanaga, Enrique and Bonvin, Camille and Hui, Lam. Measurement of the dipole in the cross-correlation function of galaxies. JCAP. 2017. doi:10.1088/1475-7516/2017/01/032. arXiv:1512.03918

work page doi:10.1088/1475-7516/2017/01/032 2017
[18]

A case study for measuring the relativistic dipole of a galaxy cross-correlation with the Dark Energy Spectroscopic Instrument

Bonvin, Camille and Lepori, Francesca and Schulz, Sebastian and Tutusaus, Isaac and Adamek, Julian and Fosalba, Pablo. A case study for measuring the relativistic dipole of a galaxy cross-correlation with the Dark Energy Spectroscopic Instrument. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad2567. arXiv:2306.04213

work page doi:10.1093/mnras/stad2567 2023
[19]

Liam and Zaldarriaga, Matias

Yoo, Jaiyul and Fitzpatrick, A. Liam and Zaldarriaga, Matias. A new perspective on galaxy clustering as a cosmological probe: General relativistic effects. 2009. doi:10.1103/PhysRevD.80.08be3514. arXiv:0907.0707

work page doi:10.1103/physrevd.80.08be3514 2009
[20]

Physical Review D , volume =

Challinor, Anthony and Lewis, Antony. The linear power spectrum of observed source number counts. 2011. doi:10.1103/PhysRevD.84.043516. arXiv:1105.5292

work page doi:10.1103/physrevd.84.043516 2011
[21]

Gravitational Lensing , year = 1990, editor =

Gravitational Redshifts and Lensing by Large Scale Structures. Gravitational Lensing , year = 1990, editor =. doi:10.1007/BFb0009230 , adsurl =

work page doi:10.1007/bfb0009230 1990
[22]

, keywords =

Gravitational redshift in galaxy clusters. , keywords =
[23]

, eprint=

Nick Kaiser , title =. , eprint=. doi:10.1093/mnras/stt1370 , year = 2013, month =

work page doi:10.1093/mnras/stt1370 2013
[24]

and Li, Baojiu

Zhao, HongSheng and Peacock, John A. and Li, Baojiu. Testing gravity theories via transverse Doppler and gravitational redshifts in galaxy clusters. Phys. Rev. D. 2013. doi:10.1103/PhysRevD.88.043013. arXiv:1206.5032

work page doi:10.1103/physrevd.88.043013 2013
[25]

Gravitational Redshift of Galaxies in Clusters from the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey

Sadeh, Iftach and Feng, Low Lerh and Lahav, Ofer. Gravitational Redshift of Galaxies in Clusters from the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. Phys. Rev. Lett. 2015. doi:10.1103/PhysRevLett.114.071103. arXiv:1410.5262

work page doi:10.1103/physrevlett.114.071103 2015
[26]

Gravitational redshift and asymmetric redshift-space distortions for stacked clusters

Cai, Yan-Chuan and Kaiser, Nick and Cole, Shaun and Frenk, Carlos. Gravitational redshift and asymmetric redshift-space distortions for stacked clusters. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx469. arXiv:1609.04864

work page doi:10.1093/mnras/stx469 2017
[27]

Gravitational

Di Dio, Enea and Castello, Sveva and Bonvin, Camille. Gravitational Redshift from Galaxy Clusters -- a Relativistic Approach. 2025. arXiv:2503.11585

work page arXiv 2025
[28]

Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum

McDonald, Patrick. Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum. JCAP. 2009. doi:10.1088/1475-7516/2009/11/026. arXiv:0907.5220

work page doi:10.1088/1475-7516/2009/11/026 2009
[29]

Zhu, Hongyu and Alam, Shadab and Croft, Rupert A. C. and Ho, Shirley and Giusarma, Elena. N-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx1644. arXiv:1709.07859

work page doi:10.1093/mnras/stx1644 2017
[30]

Alam, Shadab and Zhu, Hongyu and Croft, Rupert A. C. and Ho, Shirley and Giusarma, Elena and Schneider, Donald P. Relativistic distortions in the large-scale clustering of SDSS-III BOSS CMASS galaxies. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx1421. arXiv:1709.07855

work page doi:10.1093/mnras/stx1421 2017
[31]

On the validity of the streaming model for the redshift space correlation function in the linear regime

Fisher, Karl B. On the validity of the streaming model for the redshift space correlation function in the linear regime. Astrophys. J. 1995. doi:10.1086/175980. arXiv:astro-ph/9412081

work page doi:10.1086/175980 1995
[32]

Redshift-space distortions, pairwise velocities, and nonlinearities , journal =

Rom. Redshift-space distortions, pairwise velocities, and nonlinearities , journal =. doi:10.1103/physrevd.70.083007 , year = 2004, month =

work page doi:10.1103/physrevd.70.083007 2004
[33]

Asymmetric galaxy correlation functions

Bonvin, Camille and Hui, Lam and Gaztanaga, Enrique. Asymmetric galaxy correlation functions. Phys. Rev. D. 2014. doi:10.1103/PhysRevD.89.083535. arXiv:1309.1321

work page doi:10.1103/physrevd.89.083535 2014
[34]

Large-scale clustering of galaxies in general relativity

Jeong, Donghui and Schmidt, Fabian and Hirata, Christopher M. Large-scale clustering of galaxies in general relativity. 2012. doi:10.1103/PhysRevD.85.023504. arXiv:1107.5427

work page doi:10.1103/physrevd.85.023504 2012
[35]

Nonlinear redshift-space distortions on the full sky

Dam, Lawrence and Bonvin, Camille. Nonlinear redshift-space distortions on the full sky. Phys. Rev. D. 2023. doi:10.1103/PhysRevD.108.103505. arXiv:2307.01294

work page doi:10.1103/physrevd.108.103505 2023
[36]

Exploring redshift-space distortions in large-scale structure

Vlah, Zvonimir and White, Martin. Exploring redshift-space distortions in large-scale structure. JCAP. 2019. doi:10.1088/1475-7516/2019/03/007. arXiv:1812.02775

work page doi:10.1088/1475-7516/2019/03/007 2019
[37]

2011, MNRAS, 418, 467, doi: 10.1111/j.1365-2966.2011.19497.x

Reid, Beth A. and White, Martin. Towards an accurate model of the redshift space clustering of halos in the quasilinear regime. Mon. Not. Roy. Astron. Soc. 2011. doi:10.1111/j.1365-2966.2011.19379.x. arXiv:1105.4165

work page doi:10.1111/j.1365-2966.2011.19379.x 2011
[38]

Convolution Lagrangian perturbation theory for biased tracers

Carlson, Jordan and Reid, Beth and White, Martin. Convolution Lagrangian perturbation theory for biased tracers. Mon. Not. Roy. Astron. Soc. 2013. doi:10.1093/mnras/sts457. arXiv:1209.0780

work page doi:10.1093/mnras/sts457 2013
[39]

An analytic model for redshift-space distortions

Wang, Lile and Reid, Beth and White, Martin. An analytic model for redshift-space distortions. Mon. Not. Roy. Astron. Soc. 2014. doi:10.1093/mnras/stt1916. arXiv:1306.1804

work page doi:10.1093/mnras/stt1916 2014
[40]

Zeldovich, Ya. B. Gravitational instability: an approximate theory for large density perturbations. Astron. Astrophys. 1970

1970
[41]

The Zel'dovich approximation

White, Martin. The Zel'dovich approximation. Mon. Not. Roy. Astron. Soc. 2014. doi:10.1093/mnras/stu209. arXiv:1401.5466

work page doi:10.1093/mnras/stu209 2014
[42]

Lagrangian perturbation theory at one loop order: successes, failures, and improvements

Vlah, Zvonimir and Seljak, Uro s and Baldauf, Tobias. Lagrangian perturbation theory at one loop order: successes, failures, and improvements. Phys. Rev. D. 2015. doi:10.1103/PhysRevD.91.023508. arXiv:1410.1617

work page doi:10.1103/physrevd.91.023508 2015
[43]

Edgeworth streaming model for redshift space distortions

Uhlemann, Cora and Kopp, Michael and Haugg, Thomas. Edgeworth streaming model for redshift space distortions. Phys. Rev. D. 2015. doi:10.1103/PhysRevD.92.063004. arXiv:1503.08837

work page doi:10.1103/physrevd.92.063004 2015
[44]

Post-Recombination Universe , year = 1988, editor =

Models for the evolution of the two point correlation function. Post-Recombination Universe , year = 1988, editor =. doi:10.1007/978-94-009-3035-3_30 , adsurl =

work page doi:10.1007/978-94-009-3035-3_30 1988
[45]

Taylor, A. N. and Hamilton, A. J. S. Nonlinear cosmological power spectra in real and redshift space. Mon. Not. Roy. Astron. Soc. 1996. doi:10.1093/mnras/282.3.767. arXiv:astro-ph/9604020

work page doi:10.1093/mnras/282.3.767 1996
[46]

and Plaszczynski, S

Campagne, J.-E. and Plaszczynski, S. and Neveu, J. The Galaxy Count Correlation Function in Redshift Space Revisited. Astrophys. J. 2017. doi:10.3847/1538-4357/aa7cf8. arXiv:1703.02818

work page doi:10.3847/1538-4357/aa7cf8 2017
[47]

Fisher, K. B. and Nusser, A. The nonlinear redshift space power spectrum: omega from redshift surveys. Mon. Not. Roy. Astron. Soc. 1996. doi:10.1093/mnras/279.1.1L. arXiv:astro-ph/9510049

work page doi:10.1093/mnras/279.1.1l 1996
[48]

and Ferreira, P

Juszkiewicz, R. and Ferreira, P. G. and Feldman, H. A. and Jaffe, Andrew H. and Davis, M. Evidence for a low density universe from the relative velocities of galaxies. Science. 2000. doi:10.1126/science.287.5450.109. arXiv:astro-ph/0001041

work page doi:10.1126/science.287.5450.109 2000
[49]

afer, Bj\

Reischke, Robert and Sch\"afer, Bj\"orn Malte and Bolejko, Krzysztof and Lewis, Geraint F. and Lautsch, Max , title = ". Mon. Not. Roy. Astron. Soc. 2019. doi:10.1093/mnras/stz944. arXiv:1812.06922

work page doi:10.1093/mnras/stz944 2019
[50]

Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering

Desjacques, Vincent and Ginat, Yonadav Barry and Reischke, Robert. Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering. Mon. Not. Roy. Astron. Soc. 2021 , month =. doi:10.1093/mnras/stab1228. arXiv:2009.02036

work page doi:10.1093/mnras/stab1228 2021
[51]

Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum

Baldauf, Tobias and Seljak, Uros and Desjacques, Vincent and McDonald, Patrick. Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum. Phys. Rev. D. 2012. doi:10.1103/PhysRevD.86.083540. arXiv:1201.4827

work page doi:10.1103/physrevd.86.083540 2012
[52]

Gravity and Large-Scale Non-local Bias

Chan, Kwan Chuen and Scoccimarro, Roman and Sheth, Ravi K. Gravity and Large-Scale Non-local Bias. Phys. Rev. D. 2012. doi:10.1103/PhysRevD.85.083509. arXiv:1201.3614

work page doi:10.1103/physrevd.85.083509 2012
[53]

Bonvin, Camille and Durrer, Ruth and Gasparini, M. Alice. Fluctuations of the luminosity distance. Phys. Rev. D. 2006. doi:10.1103/PhysRevD.85.029901. arXiv:astro-ph/0511183

work page doi:10.1103/physrevd.85.029901 2006
[54]

Galaxy Bias and non-Linear Structure Formation in General Relativity

Baldauf, Tobias and Seljak, Uros and Senatore, Leonardo and Zaldarriaga, Matias. Galaxy Bias and non-Linear Structure Formation in General Relativity. JCAP. 2011. doi:10.1088/1475-7516/2011/10/031. arXiv:1106.5507

work page doi:10.1088/1475-7516/2011/10/031 2011
[55]

General and consistent statistics for cosmological observations

Mitsou, Ermis and Yoo, Jaiyul and Durrer, Ruth and Scaccabarozzi, Fulvio and Tansella, Vittorio. General and consistent statistics for cosmological observations. Phys. Rev. Res. 2020. doi:10.1103/PhysRevResearch.2.033004. arXiv:1905.01293

work page doi:10.1103/physrevresearch.2.033004 2020
[56]

Astrophys.\ J.\ Lett

On the Pattern of Perturbations of the Hubble Flow. Astrophys.\ J.\ Lett. , keywords =. doi:10.1086/185255 , adsurl =

work page doi:10.1086/185255
[57]

Galaxy Power Spectrum in General Relativity

Grimm, Nastassia and Scaccabarozzi, Fulvio and Yoo, Jaiyul and Biern, Sang Gyu and Gong, Jinn-Ouk. Galaxy Power Spectrum in General Relativity. JCAP. 2020. doi:10.1088/1475-7516/2020/11/064. arXiv:2005.06484

work page doi:10.1088/1475-7516/2020/11/064 2020
[58]

The observed galaxy power spectrum in General Relativity

Castorina, Emanuele and di Dio, Enea. The observed galaxy power spectrum in General Relativity. JCAP. 2022. doi:10.1088/1475-7516/2022/01/061. arXiv:2106.08857

work page doi:10.1088/1475-7516/2022/01/061 2022
[59]

Reimberg, Paulo H. F. and Bernardeau, Francis and Pitrou, Cyril. Redshift-space distortions with wide angular separations. JCAP. 2016. doi:10.1088/1475-7516/2016/01/048. arXiv:1506.06596

work page doi:10.1088/1475-7516/2016/01/048 2016
[60]

The Statistics of Peaks of Gaussian Random Fields,

Bardeen, James M. and Bond, J. R. and Kaiser, Nick and Szalay, A. S. The Statistics of Peaks of Gaussian Random Fields. Astrophys. J. 1986. doi:10.1086/164143

work page doi:10.1086/164143 1986
[61]

Constrained realizations of Gaussian fields - A simple algorithm

Constrained Realizations of Gaussian Fields: A Simple Algorithm. Astrophys.\ J.\ Lett. , keywords =. doi:10.1086/186160 , adsurl =

work page doi:10.1086/186160
[62]

Hamilton, A. J. S. Linear redshift distortions: A Review. Ringberg Workshop on Large Scale Structure. 1997. doi:10.1007/978-94-011-4960-0_17. arXiv:astro-ph/9708102

work page doi:10.1007/978-94-011-4960-0_17 1997
[63]

Imprints of relativistic effects on the asymmetry of the halo cross-correlation function: from linear to non-linear scales

Breton, Michel-Andr\`es and Rasera, Yann and Taruya, Atsushi and Lacombe, Osmin and Saga, Shohei. Imprints of relativistic effects on the asymmetry of the halo cross-correlation function: from linear to non-linear scales. Mon. Not. Roy. Astron. Soc. 2019. doi:10.1093/mnras/sty3206. arXiv:1803.04294

work page doi:10.1093/mnras/sty3206 2019
[64]

and others

Rasera, Y. and others. The RayGalGroupSims cosmological simulation suite for the study of relativistic effects: An application to lensing-matter clustering statistics. Astron. Astrophys. 2022. doi:10.1051/0004-6361/202141908. arXiv:2111.08745

work page doi:10.1051/0004-6361/202141908 2022
[65]

Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales

Saga, Shohei and Taruya, Atsushi and Breton, Michel-Andr\`es and Rasera, Yann. Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales. Mon. Not. Roy. Astron. Soc. 2020. doi:10.1093/mnras/staa2232. arXiv:2004.03772

work page doi:10.1093/mnras/staa2232 2020
[66]

Wide-angle redshift-space distortions at quasi-linear scales: cross-correlation functions from Zel dovich approximation

Taruya, Atsushi and Saga, Shohei and Breton, Michel-Andr\`es and Rasera, Yann and Fujita, Tomohiro. Wide-angle redshift-space distortions at quasi-linear scales: cross-correlation functions from Zel dovich approximation. Mon. Not. Roy. Astron. Soc. 2020. doi:10.1093/mnras/stz3272. arXiv:1908.03854

work page doi:10.1093/mnras/stz3272 2020
[67]

Detectability of the gravitational redshift effect from the asymmetric galaxy clustering

Saga, Shohei and Taruya, Atsushi and Breton, Michel-Andr\`es and Rasera, Yann. Detectability of the gravitational redshift effect from the asymmetric galaxy clustering. Mon. Not. Roy. Astron. Soc. 2022. doi:10.1093/mnras/stac186. arXiv:2109.06012

work page doi:10.1093/mnras/stac186 2022
[68]

, keywords =

Lepori, F. and others. Euclid: Relativistic effects in the dipole of the two-point correlation function. Astron. Astrophys. 2025. doi:10.1051/0004-6361/202452531. arXiv:2410.06268

work page doi:10.1051/0004-6361/202452531 2025
[69]

COFFE: a code for the full-sky relativistic galaxy correlation function

Tansella, Vittorio and Jelic-Cizmek, Goran and Bonvin, Camille and Durrer, Ruth. COFFE: a code for the full-sky relativistic galaxy correlation function. JCAP. 2018. doi:10.1088/1475-7516/2018/10/032. arXiv:1806.11090

work page doi:10.1088/1475-7516/2018/10/032 2018
[70]

Scale-dependent bias from primordial non-Gaussianity in general relativity

Wands, David and Slosar, Anze. Scale-dependent bias from primordial non-Gaussianity in general relativity. Phys. Rev. D. 2009. doi:10.1103/PhysRevD.79.123507. arXiv:0902.1084

work page doi:10.1103/physrevd.79.123507 2009
[71]

, keywords =

The large-scale clustering of radio galaxies. , keywords =. doi:10.1093/mnras/253.2.307 , adsurl =

work page doi:10.1093/mnras/253.2.307
[72]

Integral constraints in spectroscopic surveys

de Mattia, Arnaud and Ruhlmann-Kleider, Vanina. Integral constraints in spectroscopic surveys. JCAP. 2019. doi:10.1088/1475-7516/2019/08/036. arXiv:1904.08851

work page doi:10.1088/1475-7516/2019/08/036 2019
[73]

Impact of our local environment on cosmological statistics

Hall, Alex. Impact of our local environment on cosmological statistics. Phys. Rev. D. 2020. doi:10.1103/PhysRevD.101.043519. arXiv:1911.07855

work page doi:10.1103/physrevd.101.043519 2020
[74]

Monopole Fluctuations in Galaxy Surveys

Yoo, Jaiyul and Eisenstein, Daniel. Monopole Fluctuations in Galaxy Surveys. Astrophys. J. Lett. 2025. doi:10.3847/2041-8213/ada911. arXiv:2410.00951

work page doi:10.3847/2041-8213/ada911 2025
[75]

Physics Reports , author =

Desjacques, Vincent and Jeong, Donghui and Schmidt, Fabian. Large-Scale Galaxy Bias. Phys. Rept. 2018. doi:10.1016/j.physrep.2017.12.002. arXiv:1611.09787

work page doi:10.1016/j.physrep.2017.12.002 2018
[76]

Croft, Rupert A. C. Gravitational redshifts from large-scale structure. Mon. Not. Roy. Astron. Soc. 2013. doi:10.1093/mnras/stt1223. arXiv:1304.4124

work page doi:10.1093/mnras/stt1223 2013
[77]

, keywords =

Sheth, Ravi K. and Tormen, Giuseppe. Large scale bias and the peak background split. Mon. Not. Roy. Astron. Soc. 1999. doi:10.1046/j.1365-8711.1999.02692.x. arXiv:astro-ph/9901122

work page doi:10.1046/j.1365-8711.1999.02692.x 1999
[78]

Ginzburg, V. L. and Syrovatsk, S. I. Developments in the theory of synchrotron radiation and its reabsorption. Ann. Rev. Astron. Astrophys. 1969. doi:10.1146/annurev.aa.07.090169.002111

work page doi:10.1146/annurev.aa.07.090169.002111 1969
[79]

Radiative Processes in Astrophysics
[80]

Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

Okumura, Teppei and Seljak, Uros and Vlah, Zvonimir and Desjacques, Vincent. Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory. JCAP. 2014. doi:10.1088/1475-7516/2014/05/003. arXiv:1312.4214

work page doi:10.1088/1475-7516/2014/05/003 2014

Showing first 80 references.