Lagrangian bias in the local bias model

Noemi Frusciante (SISSA); Ravi K. Sheth (ICTP/UPenn)

RECORD

Lagrangian bias in the local bias model

Noemi Frusciante (SISSA), Ravi K. Sheth (ICTP/UPenn)

Cosmology and Nongalactic Astrophysics · Submitted 1 Aug 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,087 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.60 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field.	background 1.00	0.04	0.03	asserted 0.62
s1	We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function.	result 0.95	0.91	0.66	asserted 1.00
s2	This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function.	result 0.99	0.86	0.43	asserted 1.00
s3	In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions.	result 1.00	0.87	0.17	asserted 1.00
s4	Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit.	result 0.95	0.80	0.09	asserted 0.99
s5	In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space.	interpretation 0.94	0.57	0.17	hedged possibility 0.88
s6	We discuss why things are more complicated in practice.	limitation 0.90	0.49	0.02	unclear 0.70
s7	We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not.	interpretation 0.93	0.45	0.05	asserted 0.87
s8	We use the Lognormal model to illustrate many of our findings.	method 0.97	0.88	0.03	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 12 citations worldwide. Full citation record

An analytical model for non-local stochastic field-level galaxy bias on the sphere
astro-ph.CO 2026-10 conditional novelty 7.0 of 10

A stochastic, scale-dependent galaxy bias model on the sphere, calibrated only to two-point power spectra, reproduces the bispectrum and higher-order statistics of FLAMINGO hydrodynamical galaxies down to roughly ten ...
Disentangling modified gravity and galaxy bias with field-level inference
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

With fixed known initial phases, voxel-by-voxel Poisson likelihood on the galaxy number-counts field breaks the f(R)–bias degeneracy that power spectra cannot resolve, with voids and walls driving the gain.
Halo Stochasticity from Exclusion and non-linear Clustering
astro-ph.CO 2013-05 conditional novelty 6.0 of 10

Halo shot noise departs from the Poisson value 1/n because exclusion suppresses it and non-linear clustering enhances it, with the same low-wavenumber amplitude before and after gravitational collapse.
Peak-Background Split, Renormalization, and Galaxy Clustering
astro-ph.CO 2012-12 accept novelty 6.0 of 10

The paper proves to all orders that the coarse-graining-dependent terms in the local bias expansion of galaxy clustering resum exactly into peak-background-split bias parameters defined as derivatives of the mean trac...
Large-Scale Galaxy Bias
astro-ph.CO 2016-11 accept novelty 5.0 of 10

The paper reviews and extends the perturbative theory of galaxy bias, showing that quasi-linear galaxy clustering is captured by a finite set of bias parameters built from local gravitational observables.

How the literature uses it

3 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.