Generating Moving Field Initial Conditions with Spatially Varying Boost

Siyang Ling

REVIEW 3 major objections 5 minor 117 references

Generating Moving Field Initial Conditions with Spatially Varying Boost

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A local Lorentz-boost algorithm stamps any prescribed, spatially varying bulk velocity profile onto field initial conditions, for any Lorentz-covariant theory at speeds up to ultra-relativistic.

desk verdict A genuinely useful low-velocity boost construction with a clean derivation, wrapped in an ultra-relativistic claim that the paper does not actually support. read the letter →

arxiv 2506.23020 v1 pith:UVBDSPGM submitted 2025-06-28 physics.comp-ph astro-ph.COgr-qcmath-phmath.MP

Siyang Ling This is my paper

classification physics.comp-phastro-ph.COgr-qcmath-phmath.MP PACS 02.70.-c11.10.-z98.80.-k

keywords spatiallyvaryingboostinitialconditionsLorentzcovarianceultra-relativisticfieldssine-GordonsolitonsProcafieldSchrödinger-Poissonwavedarkmatter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a generic numerical procedure for turning any given, initially stationary field configuration into a new configuration that moves with a prescribed, spatially varying bulk velocity $v(x)$. The procedure works by performing local Lorentz boosts, encoded in a slice function $\tau(x)$ with $\nabla\tau = -v$, and it is meant to hold for any Lorentz-covariant field theory, with no restriction on the equation of motion and no need for analytic solutions. The low-velocity version is a direct local-boost formula; the relativistic version is obtained by composing infinitesimal such boosts through a bookkeeping parameter $\epsilon$, so the final data are produced by solving an initial value problem from $\epsilon=0$ to $\epsilon=1$. If the method works, simulators could control small-scale field structure and large-scale bulk motion independently, which opens new types of simulations in cosmology, condensed matter, and high-energy physics. The paper demonstrates the algorithm on ultra-relativistic Sine-Gordon breathers, a relativistic Proca field with random velocities, and a spin-1 Schrödinger-Poisson dark matter field with cosmological perturbations.

What carries the argument

The central object is the spatially varying boost equation, Eq. (5): an initial value problem in a bookkeeping parameter $\epsilon$ whose flow, started from the unmoving data at $\epsilon=0$, reshapes the field and its time derivative, with $d\tilde F_a/d\epsilon = \tau \partial_t \tilde F_a + N_{ab} \tilde F_b$ and a companion equation for $\partial_t \tilde F_a$; here $\tau(x)$ defines the local time slice, $N_{ab}$ is the generator of the field's Lorentz representation evaluated at $\epsilon\nabla\tau$, and the equation of motion supplies $\partial_t^2 \tilde F_a$. The physical input is the identification of $-\nabla\tau(x)$ with the local rapidity $w(x)=\tanh^{-1}(v)v/v$, so that composing infinitesimal spatially varying boosts gives the finite boost, and for constant $w$ the procedure reduces to an ordinary Lorentz boost. This machinery carries the argument because it defines the boosted data without ever needing the analytic solution of the field equations.

What would settle it

Take an integrable theory with known boosted solutions (for example two sine-Gordon breathers), choose a rapidity profile $w(x)$ whose gradient is comparable to the soliton width with $|w|$ above 1, solve Eq. (5) to $\epsilon=1$, and compare the output with the exact Lorentz-boosted fields on a fine grid; if the relative $L^2$ difference remains large while the same comparison for slowly varying $w$ converges to small values, the advertised ultra-relativistic generality would be refuted.

Watch

Extended reading notes

Core claim

The central claim is that, starting from arbitrary non-moving initial data $(F_a, \partial_t F_a)$ of any Lorentz-covariant field theory, the spatially varying boost defined by Eq. (5) produces new initial data whose local bulk velocity is $v(x) = -\nabla\tau(x)$ at each point, with the rapidity $w=-\nabla\tau$ acting as the affine parameter of the local boost. In the low-velocity limit the algorithm reduces to Eq. (3), where the field is evaluated on the deformed time slice $t=\tau(x)$ and then transformed by the local Lorentz representation $M_{ab}(x)$. For relativistic velocities, the algorithm integrates the bookkeeping initial value problem Eq. (5) from $\epsilon=0$ to $\epsilon=1$, treating $\tau$ and the boost generators as infinitesimal steps; this accounts for length contraction through the equation of motion and is claimed to yield the correct relativistic stress-energy tensor, with the coarse-grained momentum-to-energy ratio $q/\rho$ following the desired $v(x)$. The paper validates the claim numerically on three examples, including an ultra-relativistic case with $v \approx 0.964$.

Load-bearing premise

The claim that the algorithm works at arbitrary speeds rests on assuming that the stepped bookkeeping procedure in Eq. (5) produces data equivalent to a genuine local boost even when the velocity profile varies on the same length scale as the field structure and the speed is close to light speed.

Editorial extensions

If this is right

Soliton, kink, and string simulations can be initialized at arbitrary speeds, including ultra-relativistic ones, without relying on analytic boosted solutions; numerically defined soliton profiles formed in lattice simulations can be boosted the same way.
Cosmological and condensed-matter field simulations can assign large-scale bulk velocity fields independently of the small-scale fluctuation scale $k_*$, so that, for example, a wave dark matter field can have prescribed density and velocity perturbations while retaining a chosen characteristic wavenumber.
Random field ensembles can be boosted so that their coarse-grained stress-energy takes the perfect-fluid form $(\bar\rho+\bar p)u^\mu u^\nu + \bar p \delta^{\mu\nu}$ with $u^\mu=\gamma(1,v(x))$, provided the velocity variations are on larger scales than the field fluctuations.
The procedure can create initial data for new collision experiments, such as assigning large local velocities to a single soliton body to study deformation or rupture.
In the non-relativistic wave-dark-matter limit the boost reduces to a position-dependent phase shift $\hat\Psi \approx e^{-im\tau(x)}\Psi$, giving a numerically inexpensive way to add velocities consistent with cosmological perturbation theory.

Reading between the lines

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

Because the realized velocity is $v=-\nabla\tau$, only irrotational velocity profiles can be encoded; extending the construction to rotational flows would require a different slice connection and would make the method applicable to turbulent or vortex-bearing initial data.
The nonlinearity of the boost for nonlinear field theories means Gaussian input becomes non-Gaussian output whose spatial structure is controlled by $\tau$; this could be exploited as a tunable generator of spatially varying non-Gaussianity in simulations.
A natural stress test beyond the paper's examples is to evolve the boosted ultra-relativistic breather data into a collision and compare with the known analytic behavior of sine-Gordon solutions; agreement would extend confidence from static initial data to full dynamics.
The method could be combined with existing lattice initial-condition pipelines for early-universe phase transitions to produce moving bubble or defect networks with separate control of bulk velocity and microscopic fluctuations.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my take. The core new thing is the spatially varying boost at small velocity, Eq. (3): given a time-slice function τ(x) with ∇τ = -v, the construction produces initial data whose stress-energy matches a local Lorentz boost to O(v^2) + O(∇M F). That derivation is explicit and honest, and it gives users a practical recipe for assigning bulk velocities to fields that don't have analytic moving solutions. That alone is a real contribution, and the Proca and Schrödinger-Poisson demonstrations are sensible checks. The author also ships code, which matters.

The relativistic extension, Eq. (5), is the soft spot. Composing infinitesimal boosts through an ε-flow is a clever bookkeeping device, but the paper gives no argument that the frozen-τ exponential equals a path-ordered composition of local boosts when w varies in space. The two differ at O(w^2 ∇w). The only ultra-relativistic example, the Sine-Gordon breathers with rapidity ±2, has w varying on scales much larger than the solitons; the supplemental comparison with an ordinary boost shows 3% difference, which confirms only the quasi-uniform limit. So the abstract's 'no restriction... ultra-relativistic velocities' overstates what is shown. The method needs either a derivation or a quantitative test with w varying on the field scale at w>1.

A couple of smaller points. The genericity claim also glosses over the actual requirements: second-order-in-time equations of motion, a Lorentz representation for the field, and irrotational velocity fields. The irrotational restriction is at least acknowledged in the Discussion. The SP example uses the Galilean phase-shift limit of the boost, which is appropriate for v<<1, but the paper doesn't directly compare the resulting density and velocity perturbations to the analytic matter-dominated predictions; the spectra are shown but the text says 'consistent' without a quantitative test. That is a minor issue; the setup follows from standard perturbation theory.

Bottom line: the low-velocity part is solid and the method is likely to be used, especially by people who need to initialize field-theory simulations with bulk flows—soliton collisions, cosmic strings, wave dark matter. The ultra-relativistic generality needs more work before it should be taken at face value. A serious referee should be able to extract the missing derivation or force a properly varying-w ultra-relativistic test. I'd send it to review rather than desk reject; with a revision that addresses the ε-flow justification, it would be a useful methods paper.

Referee Report

3 major / 5 minor

Summary. The paper introduces a numerical algorithm, the "spatially varying boost", for generating initial conditions of Lorentz-covariant field theories with a prescribed, spatially varying bulk velocity. For non-relativistic velocities, it proposes a local Lorentz-boost formula (Eq. 3) in which the constant-time hypersurface is replaced by a graph t = τ(x) with ∇τ = -v(x), and it derives an error bound for the stress-energy tensor (Eq. 4). For relativistic velocities, it extends the method by introducing a bookkeeping parameter ε and solving an initial-value problem (Eq. 5) from ε = 0 to ε = 1, interpreting -∇τ(x) as a spatially varying rapidity. The method is demonstrated on three examples: ultra-relativistic Sine-Gordon breathers, a relativistic transverse Proca field with large-scale velocity perturbations, and a spin-1 Schrödinger-Poisson field with cosmological density and velocity perturbations. Code is made available.

Significance. If the central claim holds, the algorithm would be a broadly useful tool for field-theory simulations, allowing one to independently prescribe small-scale field structure and large-scale bulk motion. The low-velocity derivation in Eqs. (3)-(4) is clean and includes explicit error terms, the Schrödinger-Poisson application via the phase shift (Eq. 12) is elegant and practically valuable, and the paper ships reproducible code. However, the advertised headline capability—generating arbitrary ultra-relativistic velocity profiles for arbitrary fields—is not established by the evidence presented. The soundness of the low-velocity regime does not automatically transfer to the ultra-relativistic regime, and the paper's own demonstrations do not exercise the regime where the claim is distinctive.

major comments (3)

[Spatially varying boost, Eq. (5)] The ε-flow extension to relativistic rapidities is asserted rather than derived. For constant rapidity w, integrating Eq. (5) to ε=1 reproduces an ordinary Lorentz boost, but for non-constant w the flow uses a frozen-τ generator and is not the path-ordered composition of local boosts evaluated at successively transported positions. The difference is at least O(w²∇w) and is not estimated anywhere. Since this is the load-bearing step for the abstract's 'no restriction... ultra-relativistic' claim, the manuscript needs either a derivation with an error estimate or a quantitative test in a regime where w varies on the same scale as the field structure.
[Ultra-relativistic Sine-Gordon soliton (Eq. 8, Supplemental I.A)] The sole ultra-relativistic example does not test the regime the method claims to handle. With L=40 and breather width ~1, the rapidity w(x) = -∂xτ(x) = 2 sin(2πx/L) varies on a scale much larger than the solitons, and its derivative vanishes at both breather locations, so the configuration is essentially a superposition of two uniform boosts. The text itself states that the generated initial data are 'essentially identical' to superposing two uniformly boosted breathers, and the Supplemental Material reports relative L2 differences from ordinary boosts of about 3% (L=40) and 0.5% (L=100). This confirms only the near-uniform-w limit and leaves the ultra-relativistic, strongly varying-w claim unsupported.
[Spatially varying boost, paragraph after Eq. (5)] The claim that after a relativistic boost 'the bulk velocity q(x)/ρ(x) of the boosted field is still expected to be ∼ v(x)' is supported only by a heuristic cancellation argument and by unspecified 'numerical experiments'. No error term analogous to the O(v²)+O(∇M F) bound in Eq. (4) is provided for the relativistic case. Because the paper's central utility is prescribing q/ρ, the authors should either supply an analytic bound or directly measure q/ρ versus tanh(w) in a configuration where w varies on the field's characteristic scale, and report the disagreement.

minor comments (5)

[Abstract / Introduction] The claim that the algorithm has 'no restriction on the type of the field' is too broad: the derivation assumes a Lorentz-covariant field theory with a linear representation Mab of the Lorentz group, and gauge fields require gauge fixing as done for the Proca example. Please qualify the claim.
[Eq. (5)] The notation Λ(ε∇τ(x)) is used without definition; please specify that it denotes the Lorentz boost with rapidity vector ε∇τ(x), so that the derivative defining Nab(x) is unambiguous.
[After Eq. (5)] The sentence 'The algorithm is thus valid for w > 1' is confusing; presumably it means the algorithm applies for rapidities w that can be greater than 1, i.e., ultra-relativistic velocities. Please reword.
[Random Fields, Eq. (6)] The criterion ∇v/v ≪ ∇Fa/Fa is not defined precisely for multi-component or gauge fields; the quantity ∇Fa/Fa is component- and gauge-dependent. State the criterion in terms of the characteristic wavenumbers of the field and the velocity profile, as is done informally later in the section.
[Spin-1 wave dark matter, Eq. (12)] The phase-shift expression e^{-imτ(x)} requires care with the FRW time coordinate and the ansatz (10) that contains a(t); please specify whether τ is conformal time and how the scale factor enters, so that the dimensional consistency of mτ(x) is explicit.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the boost construction is defined by its own equations and tested against external/standard criteria; the only self-citations are auxiliary, and the limited ultra-relativistic validation is an evidence gap, not self-reference.

full rationale

Walking the derivation chain shows no step in which a claimed output is identical to an input by construction. Eq. (3) is introduced as a definition of locally boosted initial data; Eq. (4) then derives the stress-energy transformation and identifies the O(v^2) and O((nabla M)F) errors, so the low-velocity stress-energy statement is a derived consequence rather than an assumed input. Eq. (5) is likewise defined as the epsilon-flow of the infinitesimal boost; for constant rapidity it reproduces an ordinary Lorentz boost by construction, and for non-constant rapidity the paper does not claim exactness but instead appeals to numerical checks. The Sine-Gordon validation compares the generated data against an ordinary boosted breather and against the local velocity q/rho; the Proca validation compares spectra before and after boost against independent expectations; the spin-1 SP demonstration chooses tau from the cosmological continuity equation, so the velocity output matches the input by construction, but the text presents this as initial-condition generation consistent with perturbation theory rather than as a prediction of perturbation theory, which is not circular. The self-citations (refs. [58] and [114]) provide auxiliary random-field construction tools and motivation, and they are not load-bearing for the boost algorithm itself. The genuine weakness, that the only ultra-relativistic test has rapidity varying on scales much larger than the soliton width and is therefore close to a superposition of uniform boosts, is an evidentiary or completeness limitation, not circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The algorithm itself has no fitted parameters; all listed constants are user inputs to the demonstrations, chosen for visualization or to illustrate regimes. The only ad hoc premise is the validity of the relativistic ε-composition (Eq. 5). No new physical entities are introduced.

free parameters (4)

Sine-Gordon rapidity profile amplitude = 2 L/(2π)
τ(x)=2 cos(2πx/L)L/(2π) sets the local rapidity w(x)=-∂xτ. Chosen by hand for the collision demo, not fitted to data.
Sine-Gordon breather frequency = ω = 0.2
Frequency of the breather solutions used in the demonstration; a user input.
Proca spectrum constants = C1, C2 with sqrt(<f^2>)=0.1m
Constants fixing the random-field amplitudes and the velocity perturbation scale; chosen for the demo, not fitted.
SP perturbation amplitude = A_s = 2e-6 (enhanced)
Amplitude of the scale-invariant cosmological perturbation input; the text states it is enhanced relative to observed values for visualization.

assumptions (5)

domain assumption The field theory is Lorentz covariant and the fields carry a representation M_ab(Λ) of the Lorentz group.
Invoked in Eqs. (1)-(3); required for any Lorentz boost to be defined. Standard for relativistic field theories.
domain assumption The equation of motion supplies ∂_t^2 F as a functional of F and ∂_t F (second-order-in-time dynamics).
Necessary to evolve Eq. (5) in the bookkeeping parameter ε; holds for Klein-Gordon, Sine-Gordon, Proca, and Schrödinger-Poisson systems.
ad hoc to paper Solving the ε-initial value problem, Eq. (5), from ε=0 to 1 yields the correct boosted initial data for arbitrary spatially varying rapidity.
The central unproved premise of the relativistic extension. The paper gives intuition and cites numerical support, but no derivation or quantitative validation for strongly varying ultra-relativistic profiles.
domain assumption The separation of scales condition ∇v/v << ∇F/F holds for the random-field ensembles considered.
Eq. (6) and surrounding text require this to identify the boosted stress-energy as a perfect fluid with bulk velocity v(x).
domain assumption The cosmological perturbation theory results in Eq. (13), taken from ref. [109], are correct and applicable.
Used to define the target density and velocity perturbations in the spin-1 wave dark matter example.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Generating Moving Field Initial Conditions with Spatially Varying Boost." pith.science (2026). https://pith.science/paper/UVBDSPGM

@misc{pith2026250623020,
  author       = {Pith},
  title        = {Pith review of: Generating Moving Field Initial Conditions with Spatially Varying Boost},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UVBDSPGM}},
  note         = {Machine review of arXiv:2506.23020}
}

abstract

We introduce a novel class of algorithms, the ``spatially varying boost'', for generating dynamical field initial conditions with prescribed bulk velocities. Given (non-moving) initial field data, the algorithm generates new initial data with the given velocity profile by performing local Lorentz boosts. This algorithm is generic, with no restriction on the type of the field, the equation of motion, and can endow fields with ultra-relativistic velocities. This algorithm enables new simulations in different branches of physics, including cosmology and condensed matter physics. For demonstration, we used this algorithm to (1) boost two Sine-Gordon solitons to ultra-relativistic speeds for subsequent collision, (2) generate a relativistic transverse Proca field with random velocities, and (3) set up a spin-$1$ Schr\"{o}dinger-Poisson field with velocity and density perturbations consistent with dark matter in matter dominated universe.

Figures

Figures reproduced from arXiv: 2506.23020 by the authors.

**Figure 2.** FIG. 2. The Sine-Gordon initial data before and after boost. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 2.** fig. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Figures from the paper (5 more)

**Figure 3.** Figure 3: FIG. 3. Snapshot of the Proca field overdensity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]

**Figure 4.** Figure 4: FIG. 4. Snapshot of energy overdensity and momentum den [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 1.** Figure 1: FIG. 1. Information on the stress-energy tensor of the boosted Sine-Gordon field. The left panel gives energy and momentum [PITH_FULL_IMAGE:figures/full_fig_p011_1.png]

**Figure 2.** Figure 2: FIG. 2. Spectra of the Proca field, before and after boosting. [PITH_FULL_IMAGE:figures/full_fig_p012_2.png]

**Figure 3.** Figure 3: FIG. 3. Spectra of the Schr¨odinger-Poisson field, before and after boosting. [PITH_FULL_IMAGE:figures/full_fig_p013_3.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

117 extracted references · 14 canonical work pages

[1]

Efstathiou, M

G. Efstathiou, M. Davis, C. S. Frenk, and S. D. M. White, Numerical Techniques for Large Cosmological N- Body Simulations, Astrophys. J. Suppl. 57, 241 (1985)

1985
[2]

Matarrese, O

S. Matarrese, O. Pantano, and D. Saez, A General rela- tivistic approach to the nonlinear evolution of collision- less matter, Phys. Rev. D 47, 1311 (1993)

1993
[3]

Scoccimarro, Transients from initial conditions: a perturbative analysis, Mon

R. Scoccimarro, Transients from initial conditions: a perturbative analysis, Mon. Not. Roy. Astron. Soc.299, 1097 (1998), arXiv:astro-ph/9711187

arXiv 1998
[4]

Valageas, Transients from zel’dovich initial condi- 6 tions, Astron

P. Valageas, Transients from zel’dovich initial condi- 6 tions, Astron. Astrophys. 385, 761 (2002), arXiv:astro- ph/0112102

arXiv 2002
[5]

Yoshida, N

N. Yoshida, N. Sugiyama, and L. Hernquist, The evolu- tion of baryon density fluctuations in multi-component cosmological simulations, Mon. Not. Roy. Astron. Soc. 344, 481 (2003), arXiv:astro-ph/0305210

arXiv 2003
[6]

Sirko, Initial conditions to cosmological N-body sim- ulations, or how to run an ensemble of simulations, As- trophys

E. Sirko, Initial conditions to cosmological N-body sim- ulations, or how to run an ensemble of simulations, As- trophys. J. 634, 728 (2005), arXiv:astro-ph/0503106

arXiv 2005
[7]

Crocce, S

M. Crocce, S. Pueblas, and R. Scoccimarro, Tran- sients from Initial Conditions in Cosmological Simula- tions, Mon. Not. Roy. Astron. Soc. 373, 369 (2006), arXiv:astro-ph/0606505

arXiv 2006
[8]

Tatekawa and S

T. Tatekawa and S. Mizuno, Transients from initial conditions based on Lagrangian perturbation theory in N -body simulations, JCAP 12, 014, arXiv:0706.1334 [astro-ph]

arXiv

Show all 117 references

[9]

Hahn and T

O. Hahn and T. Abel, Multi-scale initial conditions for cosmological simulations, Mon. Not. Roy. Astron. Soc. 415, 2101 (2011), arXiv:1103.6031 [astro-ph.CO]

2011 arXiv
[10]

L’Huillier, C

B. L’Huillier, C. Park, and J. Kim, Effects of the initial conditions on cosmological N -body simulations, New Astron. 30, 79 (2014), arXiv:1401.6180 [astro-ph.CO]

2014 arXiv
[11]

O. Hahn, R. E. Angulo, and T. Abel, The Properties of Cosmic Velocity Fields, Mon. Not. Roy. Astron. Soc. 454, 3920 (2015), arXiv:1404.2280 [astro-ph.CO]

2015 arXiv
[12]

Fidler, C

C. Fidler, C. Rampf, T. Tram, R. Crittenden, K. Koyama, and D. Wands, General relativistic cor- rections to N -body simulations and the Zel’dovich approximation, Phys. Rev. D 92, 123517 (2015), arXiv:1505.04756 [astro-ph.CO]

2015 arXiv
[13]

Adamek, D

J. Adamek, D. Daverio, R. Durrer, and M. Kunz, Gen- eral relativity and cosmic structure formation, Nature Phys. 12, 346 (2016), arXiv:1509.01699 [astro-ph.CO]

2016 arXiv
[14]

Adamek, D

J. Adamek, D. Daverio, R. Durrer, and M. Kunz, gevo- lution: a cosmological N-body code based on Gen- eral Relativity, JCAP 07, 053, arXiv:1604.06065 [astro- ph.CO]

arXiv
[15]

Zennaro, J

M. Zennaro, J. Bel, F. Villaescusa-Navarro, C. Carbone, E. Sefusatti, and L. Guzzo, Initial Conditions for Accu- rate N-Body Simulations of Massive Neutrino Cosmolo- gies, Mon. Not. Roy. Astron. Soc. 466, 3244 (2017), arXiv:1605.05283 [astro-ph.CO]

2017 arXiv
[16]

L. H. Garrison, D. J. Eisenstein, D. Ferrer, M. V. Metch- nik, and P. A. Pinto, Improving Initial Conditions for Cosmological N -Body Simulations, Mon. Not. Roy. As- tron. Soc. 461, 4125 (2016), arXiv:1605.02333 [astro- ph.CO]

2016 arXiv
[17]

T. Tatekawa, Transients from Initial Conditions Based on Lagrangian Perturbation Theory in N - body Simulations III: The Case of GADGET-2 Code 10.1142/S0218271820500960 (2019), arXiv:1901.09210 [astro-ph.CO]

2019 arXiv
[18]

Springel, R

V. Springel, R. Pakmor, O. Zier, and M. Reinecke, Sim- ulating cosmic structure formation with the gadget-4 code, Mon. Not. Roy. Astron. Soc. 506, 2871 (2021), arXiv:2010.03567 [astro-ph.IM]

2021 arXiv
[19]

O. Hahn, C. Rampf, and C. Uhlemann, Higher or- der initial conditions for mixed baryon–CDM simula- tions, Mon. Not. Roy. Astron. Soc. 503, 426 (2021), arXiv:2008.09124 [astro-ph.CO]

2021 arXiv
[20]

Michaux, O

M. Michaux, O. Hahn, C. Rampf, and R. E. Angulo, Accurate initial conditions for cosmological N-body sim- ulations: Minimizing truncation and discreteness er- rors, Mon. Not. Roy. Astron. Soc. 500, 663 (2020), arXiv:2008.09588 [astro-ph.CO]

2020 arXiv
[21]

Barrera-Hinojosa and B

C. Barrera-Hinojosa and B. Li, GRAMSES: a new route to general relativistic N -body simulations in cos- mology. Part II. Initial conditions, JCAP 04, 056, arXiv:2001.07968 [astro-ph.CO]

2001 arXiv
[22]

R. E. Angulo and O. Hahn, Large-scale dark matter simulations, Liv. Rev. Comput. Astrophys. 8, 1 (2022), arXiv:2112.05165 [astro-ph.CO]

2022 arXiv
[23]

F. List, O. Hahn, and C. Rampf, Starting Cosmological Simulations from the Big Bang, Phys. Rev. Lett. 132, 131003 (2024), arXiv:2309.10865 [astro-ph.CO]

2024 arXiv
[24]

I. T. Iliev, G. Mellema, U.-L. Pen, H. Merz, P. R. Shapiro, and M. A. Alvarez, Simulating cosmic reioniza- tion at large scales. 1. the geometry of reionization, Mon. Not. Roy. Astron. Soc. 369, 1625 (2006), arXiv:astro- ph/0512187

2006
[25]

Mesinger, S

A. Mesinger, S. Furlanetto, and R. Cen, 21cmF AST: A Fast, Semi-Numerical Simulation of the High-Redshift 21-cm Signal, Mon. Not. Roy. Astron. Soc. 411, 955 (2011), arXiv:1003.3878 [astro-ph.CO]

2011 arXiv
[26]

Vogelsberger, S

M. Vogelsberger, S. Genel, V. Springel, P. Torrey, D. Si- jacki, D. Xu, G. F. Snyder, D. Nelson, and L. Hern- quist, Introducing the Illustris Project: Simulating the coevolution of dark and visible matter in the Uni- verse, Mon. Not. Roy. Astron. Soc. 444, 1518 (2014), arXiv:...

2014 arXiv
[27]

Molaro, R

M. Molaro, R. Dav´ e, S. Hassan, M. G. Santos, and K. Finlator, ARTIST: Fast radiative transfer for large- scale simulations of the epoch of reionisation, Mon. Not. Roy. Astron. Soc. 489, 5594 (2019), arXiv:1901.03340 [astro-ph.CO]

2019 arXiv
[28]

Maity and T

B. Maity and T. R. Choudhury, Probing the thermal his- tory during reionization using a seminumerical photon- conserving code script, Mon. Not. Roy. Astron. Soc. 511, 2239 (2022), arXiv:2110.14231 [astro-ph.CO]

2022 arXiv
[29]

H. Trac, N. Chen, I. Holst, M. A. Alvarez, and R. Cen, AMBER: A Semi-numerical Abundance Matching Box for the Epoch of Reionization, Astrophys. J. 927, 186 (2022), arXiv:2109.10375 [astro-ph.CO]

2022 arXiv
[30]

N. Chen, H. Trac, S. Mukherjee, and R. Cen, Patchy Ki- netic Sunyaev–Zel’dovich Effect with Controlled Reion- ization History and Morphology, Astrophys. J. 943, 138 (2023), arXiv:2203.04337 [astro-ph.CO]

2023 arXiv
[31]

N. Y. Gnedin and P. Madau, Modeling Cosmic Reion- ization, (2022), arXiv:2208.02260 [astro-ph.CO]

2022 arXiv
[32]

Sugiyama, KINK - ANTIKINK COLLISIONS IN THE TWO-DIMENSIONAL PHI**4 MODEL, Prog

T. Sugiyama, KINK - ANTIKINK COLLISIONS IN THE TWO-DIMENSIONAL PHI**4 MODEL, Prog. Theor. Phys. 61, 1550 (1979)

1979
[33]

R. A. Matzner, Interaction of U(1) cosmic strings: Nu- merical intercommutation, Comput. Phys. 2, 51 (1988)

1988
[34]

T. D. Lee and Y. Pang, Nontopological solitons, Phys. Rept. 221, 251 (1992)

1992
[35]

N. S. Manton and P. Sutcliffe, Topological soli- tons, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2004)

2004
[36]

Vachaspati, Kinks and Domain Walls : An Introduc- tion to Classical and Quantum Solitons(Oxford Univer- sity Press, 2007)

T. Vachaspati, Kinks and Domain Walls : An Introduc- tion to Classical and Quantum Solitons(Oxford Univer- sity Press, 2007)

2007
[37]

Achucarro and R

A. Achucarro and R. de Putter, Effective non- intercommutation of local cosmic strings at high colli- sion speeds, Phys. Rev. D 74, 121701 (2006), arXiv:hep- th/0605084

2006
[38]

Dorey, K

P. Dorey, K. Mersh, T. Romanczukiewicz, and Y. Shnir, 7 Kink-antikink collisions in the ϕ6 model, Phys. Rev. Lett. 107, 091602 (2011), arXiv:1101.5951 [hep-th]

2011 arXiv
[39]

V. A. Gani, A. E. Kudryavtsev, and M. A. Lizunova, Kink interactions in the (1+1)-dimensional ϕ6 model, Phys. Rev. D 89, 125009 (2014), arXiv:1402.5903 [hep- th]

2014 arXiv
[40]

M. A. Amin, I. Banik, C. Negreanu, and I.-S. Yang, Ultrarelativistic oscillon collisions, Phys. Rev. D 90, 085024 (2014), arXiv:1410.1822 [hep-th]

2014 arXiv
[41]

M. A. Amin, E. A. Lim, and I.-S. Yang, Clash of Kinks: Phase Shifts in Colliding Nonintegrable Solitons, Phys. Rev. Lett. 111, 224101 (2013), arXiv:1308.0605 [hep- th]

2013 arXiv
[42]

M. A. Amin, E. A. Lim, and I.-S. Yang, A scattering the- ory of ultrarelativistic solitons, Phys. Rev. D88, 105024 (2013), arXiv:1308.0606 [hep-th]

2013 arXiv
[43]

M. P. Kinach and M. W. Choptuik, Relativistic head- on collisions of U(1) gauged Q-balls, Phys. Rev. D 110, 015012 (2024), arXiv:2404.04323 [hep-th]

2024 arXiv
[44]

M. P. Kinach and M. W. Choptuik, Dynamics of U(1) gauged Q-balls in three spatial dimensions, Phys. Rev. D 110, 075033 (2024), arXiv:2408.07561 [hep-th]

2024 arXiv
[45]

Vredevoogd and S

J. Vredevoogd and S. Pratt, Universal Flow in the First fm/c at RHIC, Nucl. Phys. A 830, 515C (2009), arXiv:0907.4733 [nucl-th]

2009 arXiv
[46]

Schenke, P

B. Schenke, P. Tribedy, and R. Venugopalan, Fluc- tuating Glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett. 108, 252301 (2012), arXiv:1202.6646 [nucl-th]

2012 arXiv
[47]

C. Gale, S. Jeon, and B. Schenke, Hydrodynamic Mod- eling of Heavy-Ion Collisions, Int. J. Mod. Phys. A 28, 1340011 (2013), arXiv:1301.5893 [nucl-th]

2013 arXiv
[48]

Heinz and R

U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63, 123 (2013), arXiv:1301.2826 [nucl-th]

2013 arXiv
[49]

J. S. Moreland, J. E. Bernhard, and S. A. Bass, Alter- native ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92, 011901 (2015), arXiv:1412.4708 [nucl-th]

2015 arXiv
[50]

M. E. Carrington, A. Czajka, and S. Mrowczynski, The energy-momentum tensor at the earliest stage of rel- ativistic heavy-ion collisions, Eur. Phys. J. A 58, 5 (2022), arXiv:2012.03042 [hep-ph]

2022 arXiv
[51]

Joyce, D

M. Joyce, D. Levesque, and B. Marcos, A Method of generating initial conditions for cosmological N body simulations, Phys. Rev. D 72, 103509 (2005), arXiv:astro-ph/0411607

2005 arXiv
[52]

M. A. Amin, M. S. Delos, and M. Mirbabayi, Structure Formation with Warm White Noise: Effects of Finite Number Density and Velocity Dispersion in Particle and Wave Dark Matter, (2025), arXiv:2503.20881 [astro- ph.CO]

2025
[53]

Madelung, Quantentheorie in hydrodynamischer Form, Z

E. Madelung, Quantentheorie in hydrodynamischer Form, Z. Phys. 40, 322 (1927)

1927
[54]

E. P. S. Shellard, Cosmic String Interactions, Nucl. Phys. B 283, 624 (1987)

1987
[55]

Veltmaat, J

J. Veltmaat, J. C. Niemeyer, and B. Schwabe, Forma- tion and structure of ultralight bosonic dark matter ha- los, Phys. Rev. D 98, 043509 (2018), arXiv:1804.09647 [astro-ph.CO]

2018 arXiv
[56]

D. G. Figueroa, A. Florio, F. Torrenti, and W. Valken- burg, The art of simulating the early Universe – Part I, JCAP 04, 035, arXiv:2006.15122 [astro-ph.CO]

2006 arXiv
[57]

May and V

S. May and V. Springel, The halo mass function and fil- aments in full cosmological simulations with fuzzy dark matter, Mon. Not. Roy. Astron. Soc. 524, 4256 (2023), arXiv:2209.14886 [astro-ph.CO]

2023 arXiv
[58]

Ling and M

S. Ling and M. A. Amin, Free streaming in warm wave dark matter, JCAP 02, 025, arXiv:2408.05591 [astro- ph.CO]

arXiv
[59]

Barone, F

A. Barone, F. Esposito, C. J. Magee, and A. C. Scott, Theory and applications of the sine-gordon equation, La Rivista del Nuovo Cimento 1, 227–267 (1971)

1971
[60]

S. R. Coleman, The Quantum Sine-Gordon Equation as the Massive Thirring Model, Phys. Rev. D 11, 2088 (1975)

1975
[61]

Mandelstam, Soliton Operators for the Quantized Sine-Gordon Equation, Phys

S. Mandelstam, Soliton Operators for the Quantized Sine-Gordon Equation, Phys. Rev. D 11, 3026 (1975)

1975
[62]

C. G. Callan, Jr., Dyon-Fermion Dynamics, Phys. Rev. D 26, 2058 (1982)

1982
[63]

B. A. Malomed, The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons, Nonlinear Systems and Complexity 10, 1 (2014)

2014
[64]

Helfer, E

T. Helfer, E. A. Lim, M. A. G. Garcia, and M. A. Amin, Gravitational Wave Emission from Collisions of Com- pact Scalar Solitons, Phys. Rev. D 99, 044046 (2019), arXiv:1802.06733 [gr-qc]

2019 arXiv
[65]

J. Eby, M. Leembruggen, J. Leeney, P. Suranyi, and L. C. R. Wijewardhana, Collisions of Dark Matter Ax- ion Stars with Astrophysical Sources, JHEP 04, 099, arXiv:1701.01476 [astro-ph.CO]

arXiv
[66]

J. Y. Widdicombe, T. Helfer, and E. A. Lim, Black hole formation in relativistic Oscillaton collisions, JCAP 01, 027, arXiv:1910.01950 [astro-ph.CO]

1910 arXiv
[67]

M. A. Amin and P. Mocz, Formation, gravitational clus- tering, and interactions of nonrelativistic solitons in an expanding universe, Phys. Rev. D 100, 063507 (2019), arXiv:1902.07261 [astro-ph.CO]

2019 arXiv
[68]

P. W. Graham, J. Mardon, and S. Rajendran, Vector Dark Matter from Inflationary Fluctuations, Phys. Rev. D 93, 103520 (2016), arXiv:1504.02102 [hep-ph]

2016 arXiv
[69]

Ahmed, B

A. Ahmed, B. Grzadkowski, and A. Socha, Production of Purely Gravitational Vector Dark Matter, Acta Phys. Polon. B 50, 1809 (2019)

2019
[70]

Y. Ema, K. Nakayama, and Y. Tang, Production of purely gravitational dark matter: the case of fermion and vector boson, JHEP 07, 060, arXiv:1903.10973 [hep-ph]

1903 arXiv
[71]

Ahmed, B

A. Ahmed, B. Grzadkowski, and A. Socha, Gravita- tional production of vector dark matter, JHEP 08, 059, arXiv:2005.01766 [hep-ph]

2005 arXiv
[72]

E. W. Kolb and A. J. Long, Completely dark photons from gravitational particle production during the in- flationary era, JHEP 03, 283, arXiv:2009.03828 [astro- ph.CO]

2009 arXiv
[73]

M. Duch, B. Grzadkowski, and D. Huang, Strongly self- interacting vector dark matter via freeze-in, JHEP 01, 020, arXiv:1710.00320 [hep-ph]

arXiv
[74]

Barman, S

B. Barman, S. Bhattacharya, and B. Grzadkowski, Fee- bly coupled vector boson dark matter in effective theory, JHEP 12, 162, arXiv:2009.07438 [hep-ph]

2009 arXiv
[75]

Barman, N

B. Barman, N. Bernal, A. Das, and R. Roshan, Non- minimally coupled vector boson dark matter, JCAP 01 (01), 047, arXiv:2108.13447 [hep-ph]

arXiv
[76]

Agrawal, G

P. Agrawal, G. Marques-Tavares, and W. Xue, Open- ing up the QCD axion window, JHEP 03, 049, arXiv:1708.05008 [hep-ph]. 8

arXiv
[77]

Agrawal, N

P. Agrawal, N. Kitajima, M. Reece, T. Sekiguchi, and F. Takahashi, Relic Abundance of Dark Pho- ton Dark Matter, Phys. Lett. B 801, 135136 (2020), arXiv:1810.07188 [hep-ph]

2020 arXiv
[78]

J. A. Dror, K. Harigaya, and V. Narayan, Parametric Resonance Production of Ultralight Vector Dark Mat- ter, Phys. Rev. D 99, 035036 (2019), arXiv:1810.07195 [hep-ph]

2019 arXiv
[79]

R. T. Co, A. Pierce, Z. Zhang, and Y. Zhao, Dark Pho- ton Dark Matter Produced by Axion Oscillations, Phys. Rev. D 99, 075002 (2019), arXiv:1810.07196 [hep-ph]

2019 arXiv
[80]

Bastero-Gil, J

M. Bastero-Gil, J. Santiago, L. Ubaldi, and R. Vega- Morales, Vector dark matter production at the end of inflation, JCAP 04, 015, arXiv:1810.07208 [hep-ph]

arXiv
[81]

Salehian, M

B. Salehian, M. A. Gorji, H. Firouzjahi, and S. Muko- hyama, Vector dark matter production from inflation with symmetry breaking, Phys. Rev. D 103, 063526 (2021), arXiv:2010.04491 [hep-ph]

2021 arXiv
[82]

A. E. Nelson and J. Scholtz, Dark Light, Dark Matter and the Misalignment Mechanism, Phys. Rev. D 84, 103501 (2011), arXiv:1105.2812 [hep-ph]

2011 arXiv
[83]

Arias, D

P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Re- dondo, and A. Ringwald, WISPy Cold Dark Matter, JCAP 06, 013, arXiv:1201.5902 [hep-ph]

arXiv
[84]

Nakayama, Vector Coherent Oscillation Dark Mat- ter, JCAP 10, 019, arXiv:1907.06243 [hep-ph]

K. Nakayama, Vector Coherent Oscillation Dark Mat- ter, JCAP 10, 019, arXiv:1907.06243 [hep-ph]

1907 arXiv
[85]

Kitajima and K

N. Kitajima and K. Nakayama, Viable vector co- herent oscillation dark matter, JCAP 07, 014, arXiv:2303.04287 [hep-ph]

arXiv
[86]

L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Ul- tralight scalars as cosmological dark matter, Phys. Rev. D 95, 043541 (2017), arXiv:1610.08297 [astro-ph.CO]

2017 arXiv
[87]

W. Hu, R. Barkana, and A. Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85, 1158 (2000), arXiv:astro-ph/0003365

2000 arXiv
[88]

E. G. M. Ferreira, Ultra-light dark matter, Astron. As- trophys. Rev. 29, 7 (2021), arXiv:2005.03254 [astro- ph.CO]

2021 arXiv
[89]

Hui, Wave Dark Matter, Ann

L. Hui, Wave Dark Matter, Ann. Rev. Astron. Astro- phys. 59, 247 (2021), arXiv:2101.11735 [astro-ph.CO]

2021 arXiv
[90]

Salehian, H.-Y

B. Salehian, H.-Y. Zhang, M. A. Amin, D. I. Kaiser, and M. H. Namjoo, Beyond Schr¨ odinger-Poisson: non- relativistic effective field theory for scalar dark matter, JHEP 09, 050, arXiv:2104.10128 [astro-ph.CO]

arXiv
[91]

Salehian, M

B. Salehian, M. H. Namjoo, and D. I. Kaiser, Effective theories for a nonrelativistic field in an expanding uni- verse: Induced self-interaction, pressure, sound speed, and viscosity, JHEP 07, 059, arXiv:2005.05388 [astro- ph.CO]

2005 arXiv
[92]

M. H. Namjoo, A. H. Guth, and D. I. Kaiser, Relativistic Corrections to Nonrelativistic Effective Field Theories, Phys. Rev. D 98, 016011 (2018), arXiv:1712.00445 [hep- ph]

2018 arXiv
[93]

Braaten, A

E. Braaten, A. Mohapatra, and H. Zhang, Clas- sical Nonrelativistic Effective Field Theories for a Real Scalar Field, Phys. Rev. D 98, 096012 (2018), arXiv:1806.01898 [hep-ph]

2018 arXiv
[94]

Schive, T

H.-Y. Schive, T. Chiueh, and T. Broadhurst, Cos- mic Structure as the Quantum Interference of a Co- herent Dark Wave, Nature Phys. 10, 496 (2014), arXiv:1406.6586 [astro-ph.GA]

2014 arXiv
[95]

Schive, M.-H

H.-Y. Schive, M.-H. Liao, T.-P. Woo, S.-K. Wong, T. Chiueh, T. Broadhurst, and W. Y. P. Hwang, Un- derstanding the Core-Halo Relation of Quantum Wave Dark Matter from 3D Simulations, Phys. Rev. Lett. 113, 261302 (2014), arXiv:1407.7762 [astro-ph.GA]

2014 arXiv
[96]

Veltmaat and J

J. Veltmaat and J. C. Niemeyer, Cosmological particle- in-cell simulations with ultralight axion dark matter, Phys. Rev. D 94, 123523 (2016), arXiv:1608.00802 [astro-ph.CO]

2016 arXiv
[97]

Edwards, E

F. Edwards, E. Kendall, S. Hotchkiss, and R. Eas- ther, PyUltraLight: A Pseudo-Spectral Solver for Ultralight Dark Matter Dynamics, JCAP 10, 027, arXiv:1807.04037 [astro-ph.CO]

arXiv
[98]

X. Li, L. Hui, and G. L. Bryan, Numerical and Pertur- bative Computations of the Fuzzy Dark Matter Model, Phys. Rev. D 99, 063509 (2019), arXiv:1810.01915 [astro-ph.CO]

2019 arXiv
[99]

N. Bar, D. Blas, K. Blum, and S. Sibiryakov, Galactic rotation curves versus ultralight dark matter: Implica- tions of the soliton-host halo relation, Phys. Rev. D 98, 083027 (2018), arXiv:1805.00122 [astro-ph.CO]

2018 arXiv
[100]

X. Li, L. Hui, and T. D. Yavetz, Oscillations and Random Walk of the Soliton Core in a Fuzzy Dark Matter Halo, Phys. Rev. D 103, 023508 (2021), arXiv:2011.11416 [astro-ph.CO]

2021 arXiv
[101]

J. Chen, X. Du, E. W. Lentz, D. J. E. Marsh, and J. C. Niemeyer, New insights into the formation and growth of boson stars in dark matter halos, Phys. Rev. D 104, 083022 (2021), arXiv:2011.01333 [astro-ph.CO]

2021 arXiv
[102]

May and V

S. May and V. Springel, Structure formation in large- volume cosmological simulations of fuzzy dark matter: impact of the non-linear dynamics, Mon. Not. Roy. As- tron. Soc. 506, 2603 (2021), arXiv:2101.01828 [astro- ph.CO]

2021 arXiv
[103]

H. Y. J. Chan, E. G. M. Ferreira, S. May, K. Hayashi, and M. Chiba, The diversity of core–halo structure in the fuzzy dark matter model, Mon. Not. Roy. Astron. Soc. 511, 943 (2022), arXiv:2110.11882 [astro-ph.CO]

2022 arXiv
[104]

Jain and M

M. Jain and M. A. Amin, i-SPin: an integrator for multicomponent Schr¨ odinger-Poisson systems with self- interactions, JCAP 04, 053, arXiv:2211.08433 [astro- ph.CO]

arXiv
[105]

M. A. Amin, M. Jain, R. Karur, and P. Mocz, Small- scale structure in vector dark matter, JCAP 08 (08), 014, arXiv:2203.11935 [astro-ph.CO]

arXiv
[106]

M. Jain, W. Wanichwecharungruang, and J. Thomas, Kinetic relaxation and nucleation of Bose stars in self- interacting wave dark matter, Phys. Rev. D109, 016002 (2024), arXiv:2310.00058 [astro-ph.CO]

2024 arXiv
[107]

E. C. Nambo, A. Diez-Tejedor, E. Preciado-Govea, A. A. Roque, and O. Sarbach, Nonrelativistic Proca stars: Spherical stationary and multifrequency states, Phys. Rev. D 111, 064065 (2025), arXiv:2412.06901 [gr- qc]

2025 arXiv
[108]

Hu and N

W. Hu and N. Sugiyama, Small scale cosmological per- turbations: An Analytic approach, Astrophys. J. 471, 542 (1996), arXiv:astro-ph/9510117

1996 arXiv
[109]

Baumann, Cosmology (Cambridge University Press, 2022)

D. Baumann, Cosmology (Cambridge University Press, 2022)

2022
[110]

M. A. Amin and M. Mirbabayi, A Lower Bound on Dark Matter Mass, Phys. Rev. Lett.132, 221004 (2024), arXiv:2211.09775 [hep-ph]

2024 arXiv
[111]

R. Liu, W. Hu, and H. Xiao, Warm and fuzzy dark matter: Free streaming of wave dark matter, Phys. Rev. D 111, 023535 (2025), arXiv:2406.12970 [hep-ph]

2025 arXiv
[112]

R. Liu, W. Hu, and H. Xiao, Interference with Gravita- tional Instability: Hot and Fuzzy Dark Matter, (2025), 9 arXiv:2504.01937 [astro-ph.CO]

2025 arXiv
[113]

Capanelli, W

C. Capanelli, W. Hu, and E. McDonough, Wave Inter- ference in Self-Interacting Fuzzy Dark Matter, (2025), arXiv:2503.21865 [astro-ph.CO]

2025 arXiv
[114]

M. A. Amin, S. May, and M. Mirbabayi, Early Growth of Structure in Warm Wave Dark Matter, (2025), arXiv:2506.12131 [astro-ph.CO]

2025 arXiv
[115]

Scoccimarro, L

R. Scoccimarro, L. Hui, M. Manera, and K. C. Chan, Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity, Phys. Rev. D 85, 083002 (2012), arXiv:1108.5512 [astro- ph.CO]

2012 arXiv
[116]

W. R. Coulton, O. H. E. Philcox, and F. Villaescusa- Navarro, Signatures of a parity-violating universe, Phys. Rev. D 109, 023531 (2024), arXiv:2306.11782 [astro- ph.CO]

2024 arXiv
[117]

uncontracted

Y. Bao, L.-T. Wang, Z.-Z. Xianyu, and Y.-M. Zhong, Anatomy of Parity-violating Trispectra in Galaxy Sur- veys, (2025), arXiv:2504.02931 [astro-ph.CO]. Supplemental Material for Generating Moving Field Initial Conditions with Spatially Varying Boost Siyang Ling City University ...

2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Efstathiou, M

G. Efstathiou, M. Davis, C. S. Frenk, and S. D. M. White, Numerical Techniques for Large Cosmological N- Body Simulations, Astrophys. J. Suppl. 57, 241 (1985)

1985

[2] [2]

Matarrese, O

S. Matarrese, O. Pantano, and D. Saez, A General rela- tivistic approach to the nonlinear evolution of collision- less matter, Phys. Rev. D 47, 1311 (1993)

1993

[3] [3]

Scoccimarro, Transients from initial conditions: a perturbative analysis, Mon

R. Scoccimarro, Transients from initial conditions: a perturbative analysis, Mon. Not. Roy. Astron. Soc.299, 1097 (1998), arXiv:astro-ph/9711187

arXiv 1998

[4] [4]

Valageas, Transients from zel’dovich initial condi- 6 tions, Astron

P. Valageas, Transients from zel’dovich initial condi- 6 tions, Astron. Astrophys. 385, 761 (2002), arXiv:astro- ph/0112102

arXiv 2002

[5] [5]

Yoshida, N

N. Yoshida, N. Sugiyama, and L. Hernquist, The evolu- tion of baryon density fluctuations in multi-component cosmological simulations, Mon. Not. Roy. Astron. Soc. 344, 481 (2003), arXiv:astro-ph/0305210

arXiv 2003

[6] [6]

Sirko, Initial conditions to cosmological N-body sim- ulations, or how to run an ensemble of simulations, As- trophys

E. Sirko, Initial conditions to cosmological N-body sim- ulations, or how to run an ensemble of simulations, As- trophys. J. 634, 728 (2005), arXiv:astro-ph/0503106

arXiv 2005

[7] [7]

Crocce, S

M. Crocce, S. Pueblas, and R. Scoccimarro, Tran- sients from Initial Conditions in Cosmological Simula- tions, Mon. Not. Roy. Astron. Soc. 373, 369 (2006), arXiv:astro-ph/0606505

arXiv 2006

[8] [8]

Tatekawa and S

T. Tatekawa and S. Mizuno, Transients from initial conditions based on Lagrangian perturbation theory in N -body simulations, JCAP 12, 014, arXiv:0706.1334 [astro-ph]

arXiv