Memory of Initial Conditions in Gravitational Clustering

M. Crocce; R. Scoccimarro

REVIEW

Memory of Initial Conditions in Gravitational Clustering

M. Crocce, R. Scoccimarro

Astrophysics · Submitted 15 Sep 2005 · 14 references

Pith's verdict: The propagator formula in Eq. (41) is the durable contribution here — parameter-free, tested against simulations, and the finite-volume analysis in Section IV D is a genuine second result rather than an afterthought.

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arXiv IDastro-ph/0509419 (version 2)

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CitationM. Crocce, R. Scoccimarro. "Memory of Initial Conditions in Gravitational Clustering." arXiv:astro-ph/0509419 (2005). https://pith.science/paper/N4WCUJ2Y

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Editor's note

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The thing to take away is Eq. (41): a closed expression for the nonlinear propagator in terms of the linear power spectrum alone, plus the first measurement of that object in N-body data. That pairing is why this paper gets cited, and it holds up. The decay scales k_delta and k_theta that fall out of it became the standard estimate of BAO damping, which is a lot of mileage for a two-page derivation in Section III E. The one-loop propagator and the low-k limit in Eq. (29) are their own earlier result (ref. [6]); the new content is the principal-path resummation of Eq. (39), the exponentiation to all k, the simulation measurement, and the volume study. Credit where due: Section IV D is the best part of the paper. They notice the box dependence, turn it into a consistency check in Fig. 6, and extract a concrete requirement — roughly 240 h^-1 Mpc for 10% accuracy on the decay scale. That is a useful, checkable statement that later simulation work had to reckon with. On the soft spots, the stress-test note is half right. The step from Eq. (40) to Eq. (41) is an ansatz, and 'the only feasible way' is asserted rather than shown; the intermediate-k regime is controlled by neither limit. But the note's framing that this goes unacknowledged is wrong — Section III D says plainly that they cannot prove the omitted subset is subdominant. The classifier record lists no stated limitations; that is a miss, the limitation is right there in the text. What remains genuinely unresolved is narrower: the exponentiation is constrained (the high-k limit reproduces Eq. 39, a = 1 reduces to g_ab) but not derived. The Fig. 5 comparison is one realization of the 479 h^-1 Mpc box with no error bars, and sigma_v is cut off at that same box's k_box. That cutoff is the right choice for comparing to that simulation, and Section IV D shows they know it, but the abstract's 'no free parameters' reads better than 'no free parameters given the box.' Minor, not load-bearing — the agreement spans a decade in k and would be hard to fake. This is a solid paper with one heuristic step that is honestly flagged. Send it out.

Referee report

Significance

If it holds, the result is a genuinely useful one: Eq. (41) is an explicit, parameter-free function of the linear power spectrum and cosmology, fixed before any comparison to data, and it is falsifiable against N-body measurements. The finite-volume warning in §IV D is a practical caution for simulation design that is independent of the resummation ansatz, and the decay-scale diagnostic k_δ, k_θ gives a concrete, checkable alternative to the 4πk³P_L=1 criterion. The paper also ships a clean methodological contribution in showing that the two very different estimators of Eqs. (46) and (47) agree (Fig. 4), which is a useful validation of the cross-correlation route. The main caveat is that the central prediction rests on an interpolation ansatz whose intermediate-k behavior is not controlled by either asymptotic limit, and the empirical support in Fig. 5 is a single-realization comparison without a quoted error budget.

Major objections (4)

[§III E, Eqs. (40)–(41)] The step from Eq. (40) to Eq. (41) is the load-bearing construction of the paper, and the text asserts that 'the only feasible way to satisfy our requirements is to group things in the following way' and that 'there is a unique way to recover the latter from its one-loop expansion satisfying the right asymptotics.' The stated constraints (α in the growing part, both terms negative for all a and k) do narrow the choice, but they do not by themselves single out the particular split of h(k) and i(k) between the growing and decaying pieces in the four components of Eq. (40). Either the uniqueness should be demonstrated, or the language should be softened to 'a choice satisfying the required asymptotics,' with the empirical agreement in Fig. 5 named as the actual support. It would also help to state explicitly the check that the high-k limit of the growing part reproduces Eq. (39): with α(a) − β_g(a) = (a−1)² and f, i → −k²σ_v²/2, the growing term of G₁₁ tends to (3/5)a exp[−(a−1)²k²σ_v²/2], and the decaying term vanishes; this is a nontrivial consistency check that is currently left implicit.
[§IV C, Fig. 5] The abstract's 'remarkable agreement well into the nonlinear regime' is carried by Fig. 5, which is a single realization of the 479 h⁻¹ Mpc box with no quoted error bars or cosmic-variance estimate. The informative regime is the transition region between the one-loop and Gaussian-tail limits, and that is precisely where the comparison is least controlled. Please add an error estimate (even a jackknife or sub-volume scatter) or state explicitly what the expected realization-to-realization scatter is, and show the comparison for the medium box as well so the reader can see whether the agreement is stable. Relatedly, the prediction uses k_box = 2π/L_box of the same simulation in σ_v² (Eq. 50), so the prediction and the data share the volume input; this is physically the right thing to do, but it should be stated plainly, and the sensitivity to k_box should be quantified in the figure rather than only mentioned in §IV D.
[§IV D, final paragraph] The claim that the finite-volume suppression of the propagator and the truncation of mode-coupling terms 'compensate each other' in the power spectrum, so that power-spectrum measurements do not show the volume dependence seen in Fig. 6, is asserted qualitatively. The supporting argument ('their ratio being proportional to the linear power spectrum') is not demonstrated, and the conclusion that cosmological-parameter inference will be biased at the transition scale depends on it. Either show the cancellation explicitly (e.g., by comparing the two contributions in a smaller box) or soften the claim to a conjecture.
[§V and Fig. 7] The conclusion states that at high redshift k_nl 'can be more than an order of magnitude off from k_δ, k_θ.' At z = 3, using the paper's own numbers (k_nl = 4.02 h Mpc⁻¹ and a decay scale shifted by a factor of 2–3 from the z = 0 value of ≈0.21 h Mpc⁻¹), the ratio is closer to 7 than to 10. Please state the redshift at which the ratio first exceeds 10, or rephrase the claim with the explicit range shown in Fig. 7. This matters because the 'order of magnitude' phrasing is the headline quantitative statement of the conclusions.

Minor objections (8)

[Abstract and §V] The decay scales k_δ, k_θ are computed with σ_v² integrated from k_box (Eq. 50), so the quoted numbers are box-dependent; the abstract's 'clean definition of the validity of linear theory' should be qualified to say that the infinite-volume limit is intended and that the quoted values use k_box = 0.013 h Mpc⁻¹.
[§III D] The authors state plainly that they 'cannot prove it rigorously since we could not sum up the remaining subset and show it is indeed subdominant.' This is appropriately acknowledged; it would strengthen the paper to add a sentence in §IV C noting that the agreement in Fig. 5 is the empirical evidence that the omitted diagrams are subdominant at intermediate k, not only asymptotically.
[§III D, Eq. (32)] The sentence 'The factor of 2 in Eq. (32) is because all the branchings in Fig. 3 are a symmetric if n > 2' is garbled; 'a symmetric' should read 'symmetric.'
[§IV A, Eq. (46)] The 'ergodicity' assumption that modes within a |k| bin are independent realizations deserves one more sentence of justification, and the N(N−1) normalization and the statement that the result is real should be explained rather than asserted.
[Fig. 1 caption vs §IV] Fig. 1 uses initial conditions at z = 35, Fig. 4 uses z_initial = 5, and Fig. 5 uses z_initial = 35. Please make the initial redshifts explicit in each caption so the reader can track which comparison uses which starting point.
[Eq. (27)] The logarithmic factors ln|k−q|²/|k+q|² are singular as q → k; please state how the numerical integration handles this (principal value, analytic cancellation, or a small softening) so the one-loop curves in Fig. 4 are reproducible.
[§III F] The replacement of a(τ) by D₊(τ) in Eq. (41) is an approximation whose accuracy is not separately tested; since Fig. 5 is for Ω_m = 0.3 ΛCDM, it would help to say explicitly that Fig. 5 is the test of this approximation.
[Reference [8]] Reference [8] is listed as 'in preparation (2005)' and is cited for the power-spectrum application; this is a forward reference and is not load-bearing for the present claims, but the citation should be updated if the companion work has appeared.

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The paper

The paper claims

Gravity gradually erases the memory of the early universe, and this paper gives a parameter-free formula for how fast it does so, scale by scale and epoch by epoch.

The reading

Cosmologists assume that the density and velocity fields of the universe carry a scaled copy of their initial conditions, but that copy fades as gravitational collapse proceeds. This paper asks how fast the fading happens, and answers with a quantity called the nonlinear propagator: the average rate at which a final Fourier mode still responds to a small change in its own initial value. The authors argue this object is the cleanest measure of where linear theory stops working, and they derive an explicit closed-form expression for it by resumming a physically selected class of Feynman diagrams and exponentiating the one-loop result. The payoff is a prediction with no adjustable parameters that matches N-body simulations at redshifts $z=0$, $2$ and $5$ well past the point where ordinary perturbation theory breaks down, plus a warning that finite simulation boxes artificially prolong the memory and so mask nonlinearity.

What carries the argument

The load-bearing object is the nonlinear propagator itself, $G_{ab}(k,eta) delta_D(k-k') = <delta Psi_a(k,eta)/delta phi_b(k')>$, a two-point Green's function that measures how much of a final Fourier mode still traces its initial value. The machinery that carries the argument is a diagrammatic expansion in which the initial power spectrum, the mode-coupling vertex and the linear propagator are the three ingredients, combined with a resummation of the 'principal-path' diagrams — the trees where the main line interacts only with modes arriving straight from the initial conditions. In the large-$k$ limit the vertex matrix becomes proportional to the identity, $bar gamma_{ab} approx (1/2) k q_n x_n delta_{ab}$, which lets the $2n$ time integrals and $(2n-1)!!$ pairings collapse into a single exponential. The final step is an interpolation ansatz: write the one-loop result as a sum of a growing and a decaying term, both negative, and exponentiate each, which is claimed to be the only grouping consistent with the required asymptotics at large $a$ and large $k$.

Extended reading notes

Core claim

The central claim is that the nonlinear propagator $G_{ab}(k,a)$, defined as the ensemble-averaged functional derivative of the final density or velocity-divergence field with respect to the initial field, is the right bookkeeping device for the survival of initial conditions, and that it can be computed in closed form. The authors show that for Gaussian initial conditions $G_{ab}$ is proportional to the cross-correlation coefficient between initial and final states with the dependence on the final power spectrum divided out, which removes a known ambiguity in that coefficient. They then resum the subset of diagrams in which every interaction lies along the principal path, prove that in the large-$k$ limit each such vertex preserves the growing mode so the series sums to a Gaussian, $G_{ab}=g_{ab}(a)e^{-k^2 sigma_v^2 (a-1)^2/2}$, and interpolate to all $k$ by grouping the one-loop correction into growing and decaying pieces and exponentiating them, Eq. (41). The resulting expression, with $a$ replaced by the linear growth factor $D_+$, reproduces measurements in a $479 h^{-1}$ Mpc simulation across three redshifts without tuning. A corollary the authors emphasise is that the decay scales $k_delta = sqrt(105/61), sigma_v^{-1}$ and $k_theta = sqrt(5/9), sigma_v^{-1}$ define the nonlinear scale far better than the usual criterion $4pi k_{nl}^3 P_L(k_{nl})=1$, which at high redshift can be off by more than an order of magnitude.

Load-bearing premise

The calculation assumes that the diagrams where every interaction sits along the principal path dominate the propagator at all wavenumbers, not only in the large-$k$ limit, and the authors say outright that they could not sum the remaining diagrams to show this.

Editorial extensions

If this is right

The nonlinear power spectrum in renormalized perturbation theory can now be computed, since the propagator is the ingredient that was missing from the mode-coupling series.
Baryon acoustic oscillations should be damped by a factor near $e^{-1/2} approx 0.6$ over a smooth component at the scale $k_delta(z)$, giving a concrete estimate of where the wiggles survive.
High-redshift surveys should use $k_delta$ and $k_theta$ rather than $4pi k_{nl}^3 P_L = 1$ to decide which scales are still in the linear regime, since the standard criterion underestimates nonlinearity badly at large $z$.
Simulations built to study the high-redshift universe need boxes of roughly $240 h^{-1}$ Mpc to get the propagator decay scale right to ten percent, independent of redshift.
Finite-volume simulations suppress the propagator decay while also suppressing mode-coupling power, and the two errors cancel in the total power spectrum but not in its dependence on cosmological parameters, since their ratio tracks the linear spectrum.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the propagator is really the cleanest clock of memory loss, then the same exponential form should describe the damping of any small perturbation imprinted in the initial conditions, including non-Gaussianity shapes, so the damping factor could be measured once and applied to several observables.
The finite-volume bias identified here is a systematic that grows with the steepness of the spectrum, which suggests that small-box simulations of steep, high-redshift spectra are the most exposed, and that a box-size convergence test on the propagator is a cheap diagnostic for any simulation campaign.
Because the resummation rests on the dominance of principal-path diagrams, the intermediate-$k$ regime between one-loop and the Gaussian tail is where a numerical diagram-by-diagram summation would be most informative; a direct comparison of the omitted two-loop classes against Eq. (41) would turn the authors' stated inability to prove dominance into a quantitative error bar.
The same functional-derivative definition applied to the velocity field suggests a joint density-velocity propagator matrix whose off-diagonal entries test whether velocities decohere faster than densities, which the paper's Fig. 5 hints at but does not exploit.

Original abstract

We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions. This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature. We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonlinear regime. We also show that N-body simulations require a rather large volume to recover the correct propagator, due to the missing large-scale modes. Our results for the nonlinear propagator provide an essential element to compute the nonlinear power spectrum in RPT.

The compiled record

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,869 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.76 · 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.

We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions. This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature. We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonlinear regime. We also show that N-body simulations require a rather large volume to recover the correct propagator, due to the missing large-scale modes. Our results for the nonlinear propagator provide an essential element to compute the nonlinear power spectrum in RPT.

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	We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime.	contribution 0.66	0.53	0.07	asserted 0.99
s1	We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions.	interpretation 0.96	0.86	0.23	asserted 0.92
s2	This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature.	interpretation 0.76	0.83	0.30	asserted 1.00
s3	We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonlinear regime.	result 0.92	0.96	0.21	asserted 1.00
s4	We also show that N-body simulations require a rather large volume to recover the correct propagator, due to the missing large-scale modes.	result 0.85	0.88	0.06	asserted 1.00
s5	Our results for the nonlinear propagator provide an essential element to compute the nonlinear power spectrum in RPT.	interpretation 0.71	0.87	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from simulation or computation 0.83.

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

Figures

**Figure 1.** FIG. 1: Cross-correlation coefficients between initial and fi

**Figure 2.** Notice that the tree level diagram corresponds to the linear

**Figure 3.** FIG. 3: Tree diagrams for Ψ

**Figure 4.** FIG. 4: The density (left panel) and velocity divergence (ri

**Figure 5.** FIG. 5: Predictions for the propagator of density (left pane

**Figure 6.** FIG. 6: The dependence of the measured density (left) and vel

**Figure 7.** FIG. 7: Comparison between the nonlinear scale defined from t

Figures reproduced from arXiv:astro-ph/0509419 by the authors.

References

Works cited (14)

[6]

R. Scoccimarro, astro-ph/0008277, Ann. N.Y. Acad. Sci. 927, 13 (2000)

View on Pith Pith review arXiv 2000
[1]

D. N. Spergel et al., Astrophys. J. S. 148, 175 (2003); M. Tegmark et al., Phys. Rev. D 69, 103501 (2004)

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H. Seo, D. J. Eisenstein, Astrophys. J. 598, 720 (2003); C. Blake, K. Glazebrook, Astrophys. J. 594, 665 (2003); E. Linder, Phys. Rev. D 68, 083504 (2003); W. Hu, Z. Haiman, Phys. Rev. D 68, 063004 (2003)

View on Pith 2003
[3]

C. D. Rimes, A. J. S. Hamilton, Mon. Not. R. Astron. Soc. 360, L82 (2005)

View on Pith 2005
[4]

F. Bernardeau, S. Colombi, E. Gazta˜ naga, R. Scoccimarr o, Phys. Rept. 367, 1 (2002)

View on Pith 2002
[5]

R. Scoccimarro, Mon. Not. R. Astron. Soc. 299, 1097 (1998)

View on Pith 1998
[7]

M. Crocce, R. Scoccimarro, astro-ph/0509418 (2005) (pa perI)

View on Pith Pith review arXiv 2005
[8]

M. Crocce, R. Scoccimarro, in preparation (2005)

View on Pith 2005
[9]

R. Scoccimarro, S. Colombi, J. N. Fry, J. A. Frieman, E. Hi von, A. Melott, Astrophys. J. 496, 586 (1998)

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F. R. Bouchet, R. Juszkiewicz, S. Colombi, R. Pellat, As trophys. J. 394, L5 (1992)

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[11]

F. Bernardeau, Astrophys. J. 433, 1 (1994)

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[12]

K. Benabed, R. Scoccimarro, astro-ph/0505284 (2005)

View on Pith Pith review arXiv 2005
[13]

Fundamentally, this is also true at the nonlinear level . The nonlinear evolution of collisionless dark matter is described by the Vlasov equation, which fully preserves inf ormation since the initial phase-space density is conserved along particle trajectories, the characteristic curves of the Vlasov-Poisson system. In practice we don’t have full access ...

View on Pith
[50]

to take into account the diﬀerence between the initial spectru m of this simulation as opposed to the Lbox = 100 , 239.5 h−1 Mpc ones, but this does not alter the conclusions signiﬁcantly. Moreover, using Eqs. (48-50) one concludes that the decay lengt h of the propagators in the Lbox = 479 h Mpc−1 case is still oﬀ by about 4% compared to the inﬁnite volu...

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From the clustering of BOSS DR12 CMASS galaxies at redshift 0.59, the authors measure the expansion rate, angular diameter distance, growth rate, and matter density without assuming a dark energy model.
Modeling the Anisotropic Two-Point Galaxy Correlation Function on Small Scales and Improved Measurements of H(z), D_A(z), and f(z)sigma_8(z) from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies
astro-ph.CO 2012-09 conditional novelty 5.0 of 10

A phenomenological model of the two-dimensional galaxy correlation function, validated on mock catalogs, yields improved measurements of the Hubble parameter, angular diameter distance, and growth rate at redshift 0.3...
A critical look at cosmological perturbation theory techniques
astro-ph.CO 2009-05 accept novelty 5.0 of 10

A side-by-side test against N-body simulations shows every current analytic perturbation theory for the matter power spectrum breaks down near k about 0.1 per Mpc at redshift zero, and the newly computed 2-loop standa...
Inflation and String Theory
hep-th 2014-04 accept novelty 1.0 of 10

A survey arguing that inflation is ultraviolet-sensitive and therefore requires a quantum gravity completion, then cataloguing the string theory constructions that attempt to provide one.

How later papers used it

106 later papers cite it

Evidence: substantial. 101 of the citing papers share no author with it, and 27 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 220 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 3 used its method or tool.

Uses its method or tool 3 of 20 papers with this label

Computed its k-star following this paper and another work in its approximation of the nonlinear damping of the wiggled part in redshift space.

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: single-probe measurements from CMASS anisotropic galaxy clustering (2013) · 1.00 · paraphrased: the licence does not allow quoting
The matter power spectra are denoised on large scales based on a treatment updated from the one described in [ref] using the propagator method based on perturbation theory [ref] .

Exploring the baryonic effect signature in the Hyper Suprime-Cam Year 3 cosmic shear two-point correlations on small scales: the $S_8$ tension remains present (2024) · DarkEmulator2 · 0.92
The two-halo term is damped at quasi-linear scales following the calculation of [ref] , which means that only $P'_1H$ in HMcode depends on $p$ and $q$, not the 2-halo term (unlike the vanilla halo model).

On constraining Cosmology and the Halo Mass Function with Weak Gravitational Lensing (2023) · The Halo Model and HMcode · 0.80

How the literature uses it

78 arXiv papers cite this in 184 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

Papers citing it · 113 sentences without a confident label

Contests it 1 paper

The most generic case of scale dependent growth factors is precluded to the approaches such as [ref] , while it can be properly treated here.

Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Comparison to other approaches · contest 0.74

Builds on it 3 papers

This is a remarkable result that extends in a concrete and simple way the findings of [ref] for Gaussian initial conditions.

Multi-Point Propagators for Non-Gaussian Initial Conditions · The $α$-method · 1.00
To extend the validity of this approach to $Λ$CDM, we will reinterpret the variable $η$ as the logarithm of the linear growth factor of the growing mode, i.e. [ref] , η=ln(D/D_in) , and we redefine the field in Eq. ([ref]) as ([ φ_1 ( k, η); φ_2 ( k, η) ]) ≡e^-η ( [ δ_m ( k, η); -θ( k, η)/H f ]) ,

Next-to-leading resummations in cosmological perturbation theory · Nonlinear fluid equations and the Propagator · 0.83
When transforming the equations of motion into Fourier space as in Eq. [ref], this implies that the non-linear vertices satisfy the property γ_abc(p⃗,q⃗) = δ_ac(δ_bθq⃗·p⃗/2p^2-δ_b w_i(q⃗×p⃗)_i/2p^2)+ O(p^0) , in the limit $p⃗→0$, generalizing the result in [ref] to include vorticity.

Perturbation theory with dispersion and higher cumulants: non-linear regime · Galilean invariance · 1.00

Uses its method or tool 14 papers

To include the effect of non-linear structure formation on the BAOs, we first calculate the dewiggled power spectrum [equation] where $P_lin(k)$ is the linear matter power spectrum, $P_nw(k)$ is the no-wiggle or pure CDM power spectrum calculated using Eq.(29) from [ref] , and $k_⋆$ is marginalized over[Although $k_⋆$ can be computed by renormalization perturbation theory [ref] , doing so requires knowing the amplitude of the power spectrum, which is also marginalized over in this study.] with a flat prior over the range of 0.09 to 0.13 $h$Mpc$^-1$.

Measurements of H(z) and D_A(z) from the Two-Dimensional Two-Point Correlation Function of Sloan Digital Sky Survey Luminous Red Galaxies · Theoretical Two-Dimensional Two-Point Correlation Function · 0.99
The nonlinear damping effect of the wiggled part in redshift space can be well approximated by [ref] [equation] where $k_⋆$ could be computed by [ref] [equation] The dewiggled power spectrum is [equation] $μ_k$ is the cosine of the angle between $k$ and the line of sight (LOS).

Modeling the Anisotropic Two-Point Galaxy Correlation Function on Small Scales and Improved Measurements of H(z), D_A(z), and f(z)sigma_8(z) from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies · Modeling 2D Correlation Function for Large Scales · 0.94
The nonlinear damping effect of the “wiggled” part, in redshift space, can be well approximated following [ref] by [equation] where $μ_k$ is the cosine of the angle between $k$ and the LOS, $f$ is the growth rate, and $k_⋆$ is computed following [ref] by [equation] The dewiggled power spectrum is [equation]

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: single-probe measurements and the strong power of normalized growth rate on constraining dark energy · Theoretical Two-Dimensional Two-Point Correlation Function · 1.00

Compares with it 6 papers

We stress again that the difference between the propagator computed along the lines described in this section and the one in [ref] is entirely due to the different interpolation procedures, while the classes of diagrams resummed are exactly the same.

Next-to-leading resummations in cosmological perturbation theory · Factorization and the Crocce-Scoccimarro propagator · 0.99
In order to facilitate comparison with the known expressions for the case of a single component fluid [ref] , we define:

Cosmological perturbation theory for baryons and dark matter I: one-loop corrections in the RPT framework · Momentum integrals arising in computing $1_ab(,η)$ · 0.98
Due to the factor of $e^-η$ in the definition of the two–component field in equation [ref] the first term in the linear propagator reduces to a time independent constant matrix in contrast to the growing mode of the linear propagator of [ref] that grows as $e^η$.

Large-k Limit of Multi-Point Propagators in the RG Formalism · Evolution of Cosmic Fields · 0.97

Cites it as support 1 paper

The full validity of this identity was overlooked in early papers but was successfully checked in numerical simulations in [ref] .

Exact Results for Propagators in the Geometrical Adhesion Model · Propagators and correlators, general properties · 0.97

Cites it as background 30 papers

[ref] we review eulerian PT in the compact form discussed in [ref] , the diagrammatic approach to the PT expansion, and we recall the exact expressions for the fully nonlinear propagator and PS, which provide the starting points for their evolution equations.

Nonlinear Power Spectrum from Resummed Perturbation Theory: a Leap Beyond the BAO Scale · Introduction · 0.94
The renormalized perturbation theory (RPT) [ref] is a representative pioneering work, and since it appeared, various approaches have been subsequently proposed [ref] .

Next-to-leading resummation of cosmological perturbations via the Lagrangian picture: 2-loop correction in real and redshift spaces · Introduction · 0.91
A diversity of modeling methods have been developed ranging from simulation-based methods such as emulator [ref] , fast simulations [ref] , and machine learning [ref] to analytical methods such as Standard Perturbation Theory (SPT) [ref] , Lagrangian Perturbation Theory (LPT) [ref] , Effective-Field Theory of Large Scale Structure (EFTofLSS) [ref] , and various Renormalized Perturbation Theory (RPT) [ref] , including RegPT [ref] .

Perturbation Theory Remixed: Improved Nonlinearity Modeling beyond Standard Perturbation Theory · Introduction · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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F. Bernardeau, S. Colombi, E. Gazta˜ naga, R. Scoccimarr o, Phys. Rept. 367, 1 (2002)

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M. Crocce, R. Scoccimarro, astro-ph/0509418 (2005) (pa perI)

View on Pith Pith review arXiv 2005

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M. Crocce, R. Scoccimarro, in preparation (2005)

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R. Scoccimarro, S. Colombi, J. N. Fry, J. A. Frieman, E. Hi von, A. Melott, Astrophys. J. 496, 586 (1998)

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K. Benabed, R. Scoccimarro, astro-ph/0505284 (2005)

View on Pith Pith review arXiv 2005

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Fundamentally, this is also true at the nonlinear level . The nonlinear evolution of collisionless dark matter is described by the Vlasov equation, which fully preserves inf ormation since the initial phase-space density is conserved along particle trajectories, the characteristic curves of the Vlasov-Poisson system. In practice we don’t have full access ...

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[14] [50]

to take into account the diﬀerence between the initial spectru m of this simulation as opposed to the Lbox = 100 , 239.5 h−1 Mpc ones, but this does not alter the conclusions signiﬁcantly. Moreover, using Eqs. (48-50) one concludes that the decay lengt h of the propagators in the Lbox = 479 h Mpc−1 case is still oﬀ by about 4% compared to the inﬁnite volu...

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