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REVIEW 2 major objections 4 minor 1 cited by

CosmoLattice 2.0 adds non-minimal gravity couplings, axion–gauge dynamics, defect networks, and GPU runs about ten times faster.

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T0 review · grok-4.5

2026-07-31 04:27 UTC pith:QHT7IFEZ

load-bearing objection Solid major release of a public lattice-cosmology code: real new modules and GPU gains, with one under-documented constraint issue in the ALP sector. the 2 major comments →

arxiv 2607.24978 v1 pith:QHT7IFEZ submitted 2026-07-27 astro-ph.CO hep-ph

CosmoLattice 2.0

Jorge Baeza-Ballesteros , Daniel G. Figueroa , Adrien Florio , Nicol\'as Loayza , Franz R. Sattler , Francisco Torrent\'i , Ander Urio This is my paper
classification astro-ph.CO hep-ph
keywords lattice cosmologyCosmoLatticenon-minimal couplingaxion-gauge interactionscosmic defectsgravitational wavesRunge-Kutta integratorsGPU acceleration
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

CosmoLattice is a public C++ platform for evolving scalar and gauge fields on a lattice in an expanding universe. Version 2.0 is a major upgrade that lets users simulate physics that earlier releases could not handle: scalars non-minimally coupled to gravity through a φ²R term, axion-like fields coupled to Abelian gauge fields through φF F̃, and specialized setups for cosmic-string and domain-wall networks already close to scaling. It also supplies low-storage Runge–Kutta integrators for non-symplectic equations, an optimized gravitational-wave solver that stores only five degrees of freedom, reduced (1+1)- and (2+1)-dimensional scalar runs, arbitrary initial power spectra, and GPU support that can speed representative simulations by roughly an order of magnitude relative to CPUs. The paper presents the new modules, the algorithms behind them, and strong-scaling benchmarks, and points readers to full online documentation. A sympathetic reader cares because these tools turn previously intractable early-universe problems—axion inflation with back-reaction, long-lived defect networks, non-minimal reheating—into routine lattice experiments.

Core claim

CosmoLattice v2.0 substantially broadens both the physical scope and the computational reach of lattice cosmology by implementing non-canonical interactions (φ²R and φF F̃), specialized defect and arbitrary-spectrum initial conditions, non-symplectic low-storage Runge–Kutta integrators, a memory-reduced gravitational-wave evolution, reduced-dimension scalar dynamics, and hybrid CPU/GPU parallelization that accelerates representative runs by a factor of order ten.

What carries the argument

A modular lattice engine (TempLat) with hybrid MPI+Kokkos parallelization and low-storage Runge–Kutta integrators that stably evolve non-symplectic systems while preserving gauge constraints and allowing GPU acceleration.

Load-bearing premise

That lower-dimensional scalar runs and artificial fattening or diffusion steps for defects still reproduce the three-dimensional physical observables of interest without uncontrolled bias—something the paper itself says must be checked case by case.

What would settle it

Run the same non-minimal or axion–gauge model on both a full 3-D lattice and a reduced 2-D lattice (or with versus without fattening) and check whether spectra, energy densities, and gravitational-wave backgrounds agree within the claimed numerical accuracy; disagreement would falsify the adequacy of the reduced or artificial procedures.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Users can now lattice-evolve axion inflation through the strong back-reaction regime with self-consistent expansion and chiral gauge spectra.
  • Scaling networks of global and local strings or domain walls can be prepared and evolved with core-resolution control and defect-specific observables.
  • Non-minimally coupled scalars and future non-canonical kinetic theories become routine rather than one-off coding exercises.
  • GPU clusters can deliver order-of-ten speed-ups, making large-N or long-time parameter scans practical.
  • The same backend path is already planned to host fluids and, later, full general-relativity modules.

Where Pith is reading between the lines

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

  • Because the new integrators already handle conjugate-momentum dependence in the kernels, adding multi-field non-canonical kinetic matrices Gab(φ) should be mostly a model-file change rather than a rewrite of the time stepper.
  • The five-dof gravitational-wave scheme plus GPU scaling makes high-resolution stochastic GW background forecasts from defects or preheating competitive with dedicated wave codes.
  • If reduced-dimension validation holds for a given class of models, community-wide parameter scans that were previously limited by 3-D cost become feasible on modest hardware.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper presents CosmoLattice v2.0, a major upgrade of the public lattice-cosmology code. New physics modules cover scalars non-minimally coupled to gravity (ϕ²R, Jordan frame) and axion-like fields coupled to Abelian gauge fields (ϕFF̃), evolved with new standard and low-storage Runge–Kutta integrators. New capabilities include defect-network initialization near scaling (diffusion, fattening/extra-fattening), initialization from arbitrary external power spectra, scalar dynamics on reduced (1+1)- and (2+1)-dimensional lattices, a memory-optimized GW evolution storing 5 rather than 6 unphysical dofs, flexible spectral binning including unbinned spectra, improved snapshots, single-precision support, and a fully rewritten TempLat/Kokkos backend with hybrid MPI+GPU parallelization. Strong-scaling benchmarks on the Noctua2 cluster with two shipped models show ~50% CPU improvement over v1.3 and GPU speedups of ~5–10x depending on the model. The equations are stated and cross-referenced to companion theory reviews (The Art I/II), and constraint monitoring (Gauss, Hubble) is retained.

Significance. If the modules perform as described, this is a significant and useful release for the lattice-cosmology community: the ϕ²R and ALP-gauge sectors cover active research areas (Ricci reheating, axion inflation backreaction), the defect-initialization and arbitrary-spectrum tools address real practical bottlenecks, and the 5-dof GW algorithm and low-storage RK schemes offer concrete memory savings. Strengths worth naming: the code is public with extensive documentation and a smooth v1→v2 migration path; the physics is tied to a published companion theory monograph (The Art II); and the performance claims are backed by concrete, reproducible strong-scaling benchmarks on named hardware with named models. The honest caveats on single precision and reduced-dimension runs are also to the authors' credit.

major comments (2)
  1. [§3.2, Eq. (34)] The EOM are evolved in E–B variables with a modified Gauss law ∇·E = −(α_Λ/(a m_p))∇ϕ·B, but the manuscript never states the spatial discretization used for the ALP module, unlike §2.1 where exact lattice gauge invariance is explicitly claimed for the scalar-gauge sector. Whether the modified Gauss law and ∇·B=0 are preserved to roundoff or merely monitored depends on the discrete divergence/curl commuting correctly (automatic for spectral or staggered/link schemes, not for generic collocated finite differences). This matters most in the module's advertised strong-backreaction regime [23–25], where the source terms are largest and the chirality-resolved outputs could be contaminated by constraint drift. The fix is local: state the discrete operators used, and show (or give a specific pointer to) a constraint-violation time series from a strong-backreaction run — such data presumably alre
  2. [§3.4] The abstract and §3.4 advertise (1+1)- and (2+1)-dimensional simulations that 'mimic the three-dimensional dynamics' after modifying the initial fluctuation spectrum. The paper hedges this appropriately ('must be assessed on a case-by-case basis'), but no concrete validation artifact is given or cited for the prescription beyond a pointer to Sect. 7.1 of The Art II. Since this is a listed headline capability, please add one worked example (or a precise reference to one, e.g. in [33–35]) showing which 3D observables are reproduced quantitatively by the reduced-dimension runs and at what accuracy, so users know what the prescription does and does not guarantee.
minor comments (4)
  1. [§5.1, Fig. 1, and Abstract] The headline O(10) GPU speedup rests on the convention of equating one 128-core CPU node to a single A100 GPU, which the authors acknowledge is 'not objective'. Fig. 1 shows ~5x for lphi4 and ~10x for lphi4SU2U1. Please state in the abstract or §5 that the factor is model- and hardware-convention-dependent, and consider reporting per-device throughput to make the comparison less arbitrary.
  2. [References] Reference [42] (TempLat) is a placeholder (arXiv:2607.xxxx). Since §5 attributes major backend capabilities to TempLat and ParaFaFT, this reference must be resolved before publication, and the availability/licensing of TempLat should be stated alongside that of CosmoLattice itself.
  3. [Various] Several apparent typos: 'constrains' for 'constraints' (§3.2, twice), 'infomation' (§3.2), 'Phyton' (§4.4), 'ue to the low number' (§4.3), 'either bigger or larger than unity' (§4.3, presumably 'bigger or smaller'), and a stray ',;' after Eq. (46). Please proofread the final text.
  4. [§4.4, Eq. (44)] The two forms of the lattice power spectrum are given with and without the multiplicity factor Υ_|˜n|; please define k(˜n) explicitly at first use and clarify that the code's default output is the Type-I (exact multiplicity) convention, since users comparing to external spectra (§4.4) will need this.

Circularity Check

0 steps flagged

Software-capability paper with no derivation chain that reduces predictions to inputs; self-citations are prior method docs, not load-bearing uniqueness claims.

full rationale

CosmoLattice v2.0 is a code-release paper: it lists lattice implementations (NMC scalars, ALP–gauge, defects, reduced-D scalars), integrators, GW storage, I/O, and GPU scaling, and reports measured strong-scaling (Fig. 1). There is no fitted free parameter re-labeled as a physical prediction, no uniqueness theorem imported to forbid alternatives, and no ansatz smuggled in as a first-principles result. Inherited scalar-gauge Gauss preservation and the new modules are stated as software features; theoretical detail is deferred to The Art I/II and external refs, which document methods rather than force the v2.0 feature list by construction. Self-citations to CLv1.X and overlapping-author monographs are normal prior-art pointers for a version upgrade, not circular reductions. Honest finding: no significant circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 1 invented entities

As a methods/code paper, load-bearing content is standard FLRW lattice field theory plus engineering choices. No new fundamental physical constants are fitted. Domain assumptions are the usual continuum EOM truncated to FLRW (no full metric backreaction except linear TT GWs), and validity of reduced-dimension and artificial defect-prep dynamics.

free parameters (3)
  • Defect initialization length ℓ_str (and related diffusion/fattening parameter s) = user-chosen
    Tuneable scale controlling initial defect density and core-resolution regime (extra-fattening s=-1, fattening s=0, physical s=1); chosen by the user for each run, not predicted.
  • Program scales f_* and ω_* = user-chosen per model
    Dimensionless lattice units set by dominant field amplitude and problem timescale; conventional but run-dependent choices affecting resolution.
  • Spectral bin width Δñ = default 1
    Arbitrary radial binning for power spectra; default canonical Δñ=1, user-selectable, affects reported spectra sampling.
axioms (5)
  • domain assumption Background spacetime is spatially flat FLRW; gravitational waves are linear transverse-traceless perturbations on that background.
    Stated in §§2–2.2 and 3.1–3.2; full GR backreaction is deferred to planned v4.0.
  • domain assumption Lattice discretizations preserve gauge invariance so U(1)/SU(2) Gauss constraints remain at machine precision for canonical sectors.
    Inherited claim from v1.X (§2.1); used as correctness monitor.
  • domain assumption Non-symplectic RK methods are required/stable for kernels that depend on conjugate momenta (NMC, ALP–gauge, planned non-canonical kinetics).
    §4.1; motivated by reference to The Art I stability discussion.
  • ad hoc to paper Statistically isotropic 3D scalar dynamics can be approximated on 1D/2D lattices after adjusting the initial spectrum.
    §3.4 explicitly conditions use on case-by-case assessment.
  • domain assumption Dissipative diffusion plus fattening/extra-fattening prepares defect networks near scaling without spoiling target observables.
    §3.3 following Refs. [26–32]; artificial prep is standard in the defect literature but remains an uncontrolled modeling step.
invented entities (1)
  • TempLat lattice engine / ParaFaFT DFT backend independent evidence
    purpose: Rewritten general lattice-field C++ library providing expression algebra, Kokkos portability, and pencil-decomposed FFTs for CPU/GPU.
    Software substrate enabling hybrid parallel CosmoLattice 2.0; cited as companion software note [42].

pith-pipeline@v1.2.0-grok45-kimik3 · 38811 in / 3246 out tokens · 62369 ms · 2026-07-31T04:27:44.384879+00:00 · methodology

0 comments
read the original abstract

This paper introduces $\tt {\mathcal C}osmo{\mathcal L}attice$ $\tt v2.0$, a major upgrade that substantially broadens the physical scope and computational capabilities of the code. It introduces lattice implementations of scalar fields non-minimally coupled to gravity through $\phi^2R$, as well as axion-like fields coupled to Abelian gauge sectors as $\phi F_{\mu\nu}\widetilde F^{\mu\nu}$. It also provides new procedures for generating specialized initial conditions, including scaling networks of cosmic defects ($\it e.g.$ strings and domain walls), and fields with arbitrary power spectra. The release also incorporates low-storage Runge-Kutta integrators for non-symplectic systems (suitable $\it e.g.$ for non-minimal scalar kinetic terms as $\mathcal{G}_{ab}\partial_\mu\phi^a\partial^\mu\phi^b$), scalar-field simulations on reduced $(1+1)$- and $(2+1)$-dimensional lattices, new optimized gravitational-wave evolution, more flexible field and energy-density outputs, and GPU support that can accelerate simulations by a factor $\mathcal{O}(10)$ relative to CPU execution. Extensive documentation on the use of the code is provided on https://www.cosmolattice.com

Figures

Figures reproduced from arXiv: 2607.24978 by Adrien Florio, Ander Urio, Daniel G. Figueroa, Francisco Torrent\'i, Franz R. Sattler, Jorge Baeza-Ballesteros, Nicol\'as Loayza.

Figure 1
Figure 1. Figure 1: Strong scaling test for model lphi4 (above) and lphi4SU2U1 (below) with a range of lattice sizes N. Each setup has been run for 100 timesteps, with infrequent measurements every 50 steps (power spectra) and frequent measurements every 10 steps (averages). Simulations were performed on the Noctua2 cluster of PC2 [47], with NVIDIA A100 GPU cards. Grey dashed lines depict perfect scaling. workload is almost e… view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The art of simulating the early Universe. Part III: Scalar-Gauge-Fluid Dynamics

    astro-ph.CO 2026-07 accept novelty 5.0

    Detailed continuum-to-lattice schemes are given for perfect/imperfect fluids alone or coupled to scalars/gauges in FLRW, enabling self-consistent CosmoLattice simulations of early-Universe plasma dynamics and GWs.

Reference graph

Works this paper leans on

201 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [1]

    D. G. Figueroa, A. Florio, F. Torrenti, W. Valkenburg,CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe, Comput. Phys. Commun. 283 (2023) 108586.arXiv:2102.01031,doi:10.1016/j.cpc.2022.108586

    Pith/arXiv arXiv 2023

  2. [2]

    D. G. Figueroa, A. Florio, F. Torrenti, Present and future ofCosmoLattice, Rept. Prog. Phys. 87 (9) (2024) 094901.arXiv:2312.15056,doi:10.1088/1361-6633/ad616a

    Pith/arXiv arXiv 2024

  3. [3]

    Daverio, M

    D. Daverio, M. Hindmarsh, N. Bevis, Latfield2: A c++ library for classical lattice field theory (8 2015).arXiv:1508.05610

    Pith/arXiv arXiv 2015

  4. [4]

    K. D. Lozanov, M. A. Amin, GFiRe—Gauge Field integrator for Reheating, JCAP 04 (2020) 058. arXiv:1911.06827,doi:10.1088/1475-7516/2020/04/058

    Pith/arXiv arXiv 2020

  5. [5]

    J. T. Giblin, A. J. Tishue, Preheating in Full General Relativity, Phys. Rev. D 100 (6) (2019) 063543.arXiv:1907.10601,doi:10.1103/PhysRevD.100.063543

    Pith/arXiv arXiv 2019

  6. [6]

    Andrade, et al., GRChombo: An adaptable numerical relativity code for fundamental physics, J

    T. Andrade, et al., GRChombo: An adaptable numerical relativity code for fundamental physics, J. Open Source Softw. 6 (68) (2021) 3703.arXiv:2201.03458,doi:10.21105/joss.03703

    Pith/arXiv arXiv 2021

  7. [7]

    Buschmann, Sledgehamr: Simulating Scalar Fields with Adaptive Mesh Refinement, Astrophys

    M. Buschmann, Sledgehamr: Simulating Scalar Fields with Adaptive Mesh Refinement, Astrophys. J. 979 (2) (2025) 220.arXiv:2404.02950,doi:10.3847/1538-4357/ad9ea2

    Pith/arXiv arXiv 2025

  8. [8]

    Caravano, InflationEasy: A C++ Lattice Code for Inflation (6 2025).arXiv:2506.11797

    A. Caravano, InflationEasy: A C++ Lattice Code for Inflation (6 2025).arXiv:2506.11797

    Pith/arXiv arXiv 2025

  9. [9]

    G. N. Felder, I. Tkachev, LATTICEEASY: A Program for lattice simulations of scalar fields in an expanding universe, Comput. Phys. Commun. 178 (2008) 929–932.arXiv:hep-ph/0011159, doi:10.1016/j.cpc.2008.02.009

    Pith/arXiv arXiv 2008

  10. [10]

    G. N. Felder, CLUSTEREASY: A program for lattice simulations of scalar fields in an expanding universe on parallel computing clusters, Comput. Phys. Commun. 179 (2008) 604–606.arXiv: 0712.0813,doi:10.1016/j.cpc.2008.06.002. 21

    Pith/arXiv arXiv 2008

  11. [11]

    A. V. Frolov, DEFROST: A New Code for Simulating Preheating after Inflation, JCAP 11 (2008) 009.arXiv:0809.4904,doi:10.1088/1475-7516/2008/11/009

    Pith/arXiv arXiv 2008

  12. [12]

    Sainio, CUDAEASY - a GPU Accelerated Cosmological Lattice Program, Comput

    J. Sainio, CUDAEASY - a GPU Accelerated Cosmological Lattice Program, Comput. Phys. Com- mun. 181 (2010) 906–912.arXiv:0911.5692,doi:10.1016/j.cpc.2010.01.002

    Pith/arXiv arXiv 2010

  13. [13]

    Easther, H

    R. Easther, H. Finkel, N. Roth, PSpectRe: A Pseudo-Spectral Code for (P)reheating, JCAP 10 (2010) 025.arXiv:1005.1921,doi:10.1088/1475-7516/2010/10/025

    Pith/arXiv arXiv 2010

  14. [14]

    Huang, The Art of Lattice and Gravity Waves from Preheating, Phys

    Z. Huang, The Art of Lattice and Gravity Waves from Preheating, Phys. Rev. D 83 (2011) 123509. arXiv:1102.0227,doi:10.1103/PhysRevD.83.123509

    Pith/arXiv arXiv 2011

  15. [15]

    Sainio, PyCOOL - a Cosmological Object-Oriented Lattice code written in Python, JCAP 04 (2012) 038.arXiv:1201.5029,doi:10.1088/1475-7516/2012/04/038

    J. Sainio, PyCOOL - a Cosmological Object-Oriented Lattice code written in Python, JCAP 04 (2012) 038.arXiv:1201.5029,doi:10.1088/1475-7516/2012/04/038

    Pith/arXiv arXiv 2012

  16. [16]

    D. G. Figueroa, A. Florio, F. Torrenti, W. Valkenburg, The art of simulating the early Universe – Part I: Integration techniques and canonical cases, JCAP 04 (2021) 035.arXiv:2006.15122, doi:10.1088/1475-7516/2021/04/035

    Pith/arXiv arXiv 2021

  17. [17]

    Baeza-Ballesteros, D

    J. Baeza-Ballesteros, D. G. Figueroa, A. Florio, J. Lizarraga, N. Loayza, K. Marschall, T. Opfer- kuch, B. A. Stefanek, F. Torrentí, A. Urio, The art of simulating the early Universe. Part II. Non-canonical cases & gravitational waves, JCAP 06 (2026) 087.arXiv:2512.15627,doi: 10.1088/1475-7516/2026/06/087

    arXiv 2026

  18. [18]

    Caprini, D

    C. Caprini, D. G. Figueroa, Cosmological backgrounds of gravitational waves, Class. Quant. Grav. 35 (16) (2018) 163001.arXiv:1801.04268,doi:10.1088/1361-6382/aac608

    Pith/arXiv arXiv 2018

  19. [19]

    D. G. Figueroa, Aspects of Reheating, PhD thesis (2010)

    2010

  20. [21]

    D. G. Figueroa, A. Florio, T. Opferkuch, B. A. Stefanek, Lattice simulations of non-minimally coupled scalar fields in the Jordan frame, SciPost Phys. 15 (3) (2023) 077.arXiv:2112.08388, doi:10.21468/SciPostPhys.15.3.077

    Pith/arXiv arXiv 2023

  21. [22]

    D. G. Figueroa, T. Opferkuch, B. A. Stefanek, Ricci Reheating on the Lattice (4 2024).arXiv: 2404.17654

    Pith/arXiv arXiv 2024

  22. [23]

    D. G. Figueroa, J. Lizarraga, A. Urio, J. Urrestilla, Strong Backreaction Regime in Axion Inflation, Phys. Rev. Lett. 131 (15) (2023) 151003.arXiv:2303.17436,doi:10.1103/PhysRevLett.131. 151003

    Pith/arXiv arXiv 2023

  23. [24]

    D. G. Figueroa, J. Lizarraga, N. Loayza, A. Urio, J. Urrestilla, Nonlinear dynamics of axion inflation: A detailed lattice study, Phys. Rev. D 111 (6) (2025) 063545.arXiv:2411.16368, doi:10.1103/PhysRevD.111.063545

    arXiv 2025

  24. [25]

    Lizarraga, C

    J. Lizarraga, C. López-Mediavilla, A. Urio, Comparative study of the strong backreaction regime in axion inflation: the effect of the potential, JCAP 11 (2025) 020.arXiv:2505.19950,doi: 10.1088/1475-7516/2025/11/020

    Pith/arXiv arXiv 2025

  25. [26]

    Hindmarsh, J

    M. Hindmarsh, J. Lizarraga, J. Urrestilla, D. Daverio, M. Kunz, Scaling from gauge and scalar radiation in Abelian Higgs string networks, Phys. Rev. D 96 (2) (2017) 023525.arXiv:1703.06696, doi:10.1103/PhysRevD.96.023525. 22

    Pith/arXiv arXiv 2017

  26. [27]

    Hindmarsh, J

    M. Hindmarsh, J. Lizarraga, A. Lopez-Eiguren, J. Urrestilla, Scaling Density of Axion Strings, Phys. Rev. Lett. 124 (2) (2020) 021301.arXiv:1908.03522,doi:10.1103/PhysRevLett.124. 021301

    Pith/arXiv arXiv 2020

  27. [28]

    Hindmarsh, J

    M. Hindmarsh, J. Lizarraga, A. Lopez-Eiguren, J. Urrestilla, Approach to scaling in axion string networks, Phys. Rev. D 103 (10) (2021) 103534.arXiv:2102.07723,doi:10.1103/PhysRevD.103. 103534

    Pith/arXiv arXiv 2021

  28. [29]

    Correia, M

    J. Correia, M. Hindmarsh, J. Lizarraga, A. Lopez-Eiguren, K. Rummukainen, J. Urrestilla, Scaling density of axion strings in terasite simulations, Phys. Rev. D 111 (6) (2025) 063532.arXiv: 2410.18064,doi:10.1103/PhysRevD.111.063532

    Pith/arXiv arXiv 2025

  29. [30]

    W. H. Press, B. S. Ryden, D. N. Spergel, Dynamical Evolution of Domain Walls in an Expanding Universe, Astrophys. J. 347 (1989) 590–604.doi:10.1086/168151

    doi:10.1086/168151 1989

  30. [31]

    Bevis, M

    N. Bevis, M. Hindmarsh, M. Kunz, J. Urrestilla, CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model, Phys. Rev. D 75 (2007) 065015. arXiv:astro-ph/0605018,doi:10.1103/PhysRevD.75.065015

    Pith/arXiv arXiv 2007

  31. [32]

    J. N. Moore, E. P. S. Shellard, C. J. A. P. Martins, On the evolution of Abelian-Higgs string networks, Phys. Rev. D 65 (2002) 023503.arXiv:hep-ph/0107171,doi:10.1103/PhysRevD.65. 023503

    Pith/arXiv arXiv 2002

  32. [33]

    Antusch, D

    S. Antusch, D. G. Figueroa, K. Marschall, F. Torrenti, Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination, Phys. Lett. B 811 (2020) 135888.arXiv:2005.07563,doi:10.1016/j.physletb.2020.135888

    Pith/arXiv arXiv 2020

  33. [34]

    S.Antusch, D.G.Figueroa, K.Marschall, F.Torrenti, Characterizingthepostinflationaryreheating history: Single daughter field with quadratic-quadratic interaction, Phys. Rev. D 105 (4) (2022) 043532.arXiv:2112.11280,doi:10.1103/PhysRevD.105.043532

    Pith/arXiv arXiv 2022

  34. [35]

    Antusch, K

    S. Antusch, K. Marschall, F. Torrenti, Equation of state during (p)reheating with trilinear interac- tions, JCAP 11 (2025) 002.arXiv:2507.13465,doi:10.1088/1475-7516/2025/11/002

    Pith/arXiv arXiv 2025

  35. [36]

    M. H. Carpenter, C. A. Kennedy, Third-order 2n-storage runge-kutta schemes with error control, 1994. URLhttps://api.semanticscholar.org/CorpusID:118434708

    1994

  36. [37]

    M. H. Carpenter, C. A. Kennedy, Fourth-order 2n-storage runge-kutta schemes, 1994. URLhttps://api.semanticscholar.org/CorpusID:116658826

    1994

  37. [38]

    Bazavov, T

    A. Bazavov, T. Chuna, Efficient integration of gradient flow in lattice gauge theory and properties of low-storage commutator-free Lie group methods (1 2021).arXiv:2101.05320

    Pith/arXiv arXiv 2021

  38. [39]

    Bazavov, 2N-storage Runge-Kutta methods: Order conditions, general properties and some analytic solutions (6 2025).arXiv:2506.07359

    A. Bazavov, 2N-storage Runge-Kutta methods: Order conditions, general properties and some analytic solutions (6 2025).arXiv:2506.07359

    Pith/arXiv arXiv 2025

  39. [40]

    Bazavov, 2N-storage Runge-Kutta methods: c-reflection symmetry and factorization of the Butcher tableau (6 2025).arXiv:2506.08444

    A. Bazavov, 2N-storage Runge-Kutta methods: c-reflection symmetry and factorization of the Butcher tableau (6 2025).arXiv:2506.08444

    Pith/arXiv arXiv 2025

  40. [41]

    D. G. Figueroa, K. Marschall, A. S. Midiri, A. Roper Pol, The art of simulating the early Universe. Part III. Scalar-Gauge-Fluid Dynamics (2026).arXiv:2607.24567

    Pith/arXiv arXiv 2026

  41. [42]

    Florio, F

    A. Florio, F. R. Sattler, TempLat (2026).arXiv:2607.xxxx. 23

    2026

  42. [43]

    H. C. Edwards, C. R. Trott, D. Sunderland, Kokkos: Enabling manycore performance portability through polymorphic memory access patterns, Journal of Parallel and Distributed Computing 74 (12) (2014) 3202 – 3216, domain-Specific Languages and High-Level Frameworks for High- Performance Computing.doi:https://doi.org/10.1016/j.jpdc.2014.07.003. URLhttp://www....

    doi:10.1016/j.jpdc.2014.07.003 2014

  43. [44]

    Trott, L

    C. Trott, L. Berger-Vergiat, D. Poliakoff, S. Rajamanickam, D. Lebrun-Grandie, J. Madsen, N. Al Awar, M. Gligoric, G. Shipman, G. Womeldorff, The kokkos ecosystem: Comprehensive performance portability for high performance computing, Computing in Science Engineering 23 (5) (2021) 10–18.doi:10.1109/MCSE.2021.3098509

    arXiv 2021

  44. [45]

    C. R. Trott, D. Lebrun-Grandié, D. Arndt, J. Ciesko, V. Dang, N. Ellingwood, R. Gayatri, E. Har- vey, D. S. Hollman, D. Ibanez, N. Liber, J. Madsen, J. Miles, D. Poliakoff, A. Powell, S. Raja- manickam, M. Simberg, D. Sunderland, B. Turcksin, J. Wilke, Kokkos 3: Programming model extensions for the exascale era, IEEE Transactions on Parallel and Distribut...

    arXiv 2022

  45. [46]

    Dalcín, M

    L. Dalcín, M. Mortensen, D. E. Keyes, Fast parallel multidimensional FFT using advanced MPI, CoRR abs/1804.09536 (2018).arXiv:1804.09536. URLhttp://arxiv.org/abs/1804.09536

    Pith/arXiv arXiv 2018

  46. [47]

    Bauer, T

    C. Bauer, T. Kenter, M. Lass, L. Mazur, M. Meyer, H. Nitsche, H. Riebler, R. Schade, M. Schwarz, N. Winnwa, A. Wiens, X. Wu, C. Plessl, J. Simon, Noctua 2 supercomputer, Journal of large-scale research facilities JLSRF 9 (2024).doi:https://doi.org/10.17815/jlsrf-8-187

    doi:10.17815/jlsrf-8-187 2024

  47. [48]

    Caravano, E

    A. Caravano, E. Komatsu, K. D. Lozanov, J. Weller, Lattice simulations of axion-U(1) inflation, Phys. Rev. D 108 (4) (2023) 043504.arXiv:2204.12874,doi:10.1103/PhysRevD.108.043504

    Pith/arXiv arXiv 2023

  48. [49]

    Sharma, A

    R. Sharma, A. Brandenburg, K. Subramanian, A. Vikman, Lattice simulations of axion-U(1) in- flation: gravitational waves, magnetic fields, and scalar statistics, JCAP 05 (2025) 079.arXiv: 2411.04854,doi:10.1088/1475-7516/2025/05/079

    Pith/arXiv arXiv 2025

  49. [50]

    Caravano, K

    A. Caravano, K. Inomata, S. Renaux-Petel, Inflationary Butterfly Effect: Nonperturbative Dy- namics from Small-Scale Features, Phys. Rev. Lett. 133 (15) (2024) 151001.arXiv:2403.12811, doi:10.1103/PhysRevLett.133.151001

    Pith/arXiv arXiv 2024

  50. [51]

    Caravano, M

    A. Caravano, M. Peloso, Unveiling the nonlinear dynamics of a rolling axion during inflation, JCAP 01 (2025) 104.arXiv:2407.13405,doi:10.1088/1475-7516/2025/01/104

    Pith/arXiv arXiv 2025

  51. [52]

    Jamieson, A

    D. Jamieson, A. Caravano, E. Komatsu, Primordial power spectrum and bispectrum from lattice simulations of axion-U(1) inflation, Phys. Rev. D 112 (10) (2025) 103531.arXiv:2507.22285, doi:10.1103/3zml-71jd

    arXiv 2025

  52. [53]

    J. H. Traschen, R. H. Brandenberger, Particle Production During Out-of-equilibrium Phase Tran- sitions, Phys. Rev. D 42 (1990) 2491–2504.doi:10.1103/PhysRevD.42.2491

    doi:10.1103/physrevd.42.2491 1990

  53. [54]

    Kofman, A

    L. Kofman, A. D. Linde, A. A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195–3198.arXiv:hep-th/9405187,doi:10.1103/PhysRevLett.73.3195

    Pith/arXiv arXiv 1994

  54. [55]

    Shtanov, J

    Y. Shtanov, J. H. Traschen, R. H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51 (1995) 5438–5455.arXiv:hep-ph/9407247,doi:10.1103/PhysRevD.51.5438

    Pith/arXiv arXiv 1995

  55. [56]

    D. I. Kaiser, Post inflation reheating in an expanding universe, Phys. Rev. D 53 (1996) 1776–1783. arXiv:astro-ph/9507108,doi:10.1103/PhysRevD.53.1776

    Pith/arXiv arXiv 1996

  56. [57]

    Kofman, A

    L. Kofman, A. D. Linde, A. A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258–3295.arXiv:hep-ph/9704452,doi:10.1103/PhysRevD.56.3258. 24

    Pith/arXiv arXiv 1997

  57. [58]

    P. B. Greene, L. Kofman, A. D. Linde, A. A. Starobinsky, Structure of resonance in preheating after inflation, Phys. Rev. D 56 (1997) 6175–6192.arXiv:hep-ph/9705347,doi:10.1103/PhysRevD. 56.6175

    Pith/arXiv arXiv 1997

  58. [59]

    D. I. Kaiser, Preheating in an expanding universe: Analytic results for the massless case, Phys. Rev. D 56 (1997) 706–716.arXiv:hep-ph/9702244,doi:10.1103/PhysRevD.56.706

    Pith/arXiv arXiv 1997

  59. [60]

    D. I. Kaiser, Resonance structure for preheating with massless fields, Phys. Rev. D 57 (1998) 702–711.arXiv:hep-ph/9707516,doi:10.1103/PhysRevD.57.702

    Pith/arXiv arXiv 1998

  60. [61]

    P. B. Greene, L. Kofman, Preheating of fermions, Phys. Lett. B 448 (1999) 6–12.arXiv:hep-ph/ 9807339,doi:10.1016/S0370-2693(99)00020-9

    work page doi:10.1016/s0370-2693(99)00020-9 1999

  61. [62]

    P. B. Greene, L. Kofman, On the theory of fermionic preheating, Phys. Rev. D 62 (2000) 123516. arXiv:hep-ph/0003018,doi:10.1103/PhysRevD.62.123516

    Pith/arXiv arXiv 2000

  62. [63]

    Peloso, L

    M. Peloso, L. Sorbo, Preheating of massive fermions after inflation: Analytical results, JHEP 05 (2000) 016.arXiv:hep-ph/0003045,doi:10.1088/1126-6708/2000/05/016

    Pith/arXiv arXiv 2000

  63. [64]

    Berges, D

    J. Berges, D. Gelfand, J. Pruschke, Quantum theory of fermion production after inflation, Phys. Rev. Lett. 107 (2011) 061301.arXiv:1012.4632,doi:10.1103/PhysRevLett.107.061301

    Pith/arXiv arXiv 2011

  64. [65]

    Enqvist, D

    K. Enqvist, D. G. Figueroa, R. N. Lerner, Curvaton Decay by Resonant Production of the Standard Model Higgs, JCAP 01 (2013) 040.arXiv:1211.5028,doi:10.1088/1475-7516/2013/01/040

    Pith/arXiv arXiv 2013

  65. [66]

    D. G. Figueroa, J. Garcia-Bellido, F. Torrenti, Decay of the standard model Higgs field after inflation, Phys. Rev. D 92 (8) (2015) 083511.arXiv:1504.04600,doi:10.1103/PhysRevD.92. 083511

    Pith/arXiv arXiv 2015

  66. [67]

    B. A. Bassett, D. I. Kaiser, R. Maartens, General relativistic preheating after inflation, Phys. Lett. B 455 (1999) 84–89.arXiv:hep-ph/9808404,doi:10.1016/S0370-2693(99)00478-5

    Pith/arXiv arXiv 1999

  67. [68]

    B. A. Bassett, F. Tamburini, D. I. Kaiser, R. Maartens, Metric preheating and limitations of linearized gravity. 2., Nucl. Phys. B 561 (1999) 188–240.arXiv:hep-ph/9901319,doi:10.1016/ S0550-3213(99)00495-2

    Pith/arXiv arXiv 1999

  68. [69]

    B. A. Bassett, C. Gordon, R. Maartens, D. I. Kaiser, Restoring the sting to metric preheating, Phys. Rev. D 61 (2000) 061302.arXiv:hep-ph/9909482,doi:10.1103/PhysRevD.61.061302

    Pith/arXiv arXiv 2000

  69. [70]

    Finelli, R

    F. Finelli, R. H. Brandenberger, Parametric amplification of metric fluctuations during reheating in two field models, Phys. Rev. D 62 (2000) 083502.arXiv:hep-ph/0003172,doi:10.1103/ PhysRevD.62.083502

    Pith/arXiv arXiv 2000

  70. [71]

    Chambers, A

    A. Chambers, A. Rajantie, Lattice calculation of non-Gaussianity from preheating, Phys. Rev. Lett. 100 (2008) 041302, [Erratum: Phys.Rev.Lett. 101, 149903 (2008)].arXiv:0710.4133,doi: 10.1103/PhysRevLett.100.041302

    Pith/arXiv arXiv 2008

  71. [72]

    J. R. Bond, A. V. Frolov, Z. Huang, L. Kofman, Non-Gaussian Spikes from Chaotic Billiards in Inflation Preheating, Phys. Rev. Lett. 103 (2009) 071301.arXiv:0903.3407,doi:10.1103/ PhysRevLett.103.071301

    Pith/arXiv arXiv 2009

  72. [73]

    Linde, S

    A. Linde, S. Mooij, E. Pajer, Gauge field production in supergravity inflation: Local non- Gaussianity and primordial black holes, Phys. Rev. D 87 (10) (2013) 103506.arXiv:1212.1693, doi:10.1103/PhysRevD.87.103506

    Pith/arXiv arXiv 2013

  73. [74]

    S. V. Imrith, D. J. Mulryne, A. Rajantie, Primordial curvature perturbation from lattice simu- lations, Phys. Rev. D 100 (4) (2019) 043543.arXiv:1903.07487,doi:10.1103/PhysRevD.100. 043543. 25

    Pith/arXiv arXiv 2019

  74. [75]

    Musoke, S

    N. Musoke, S. Hotchkiss, R. Easther, Lighting the Dark: Evolution of the Postinflationary Universe, Phys. Rev. Lett. 124 (6) (2020) 061301.arXiv:1909.11678,doi:10.1103/PhysRevLett.124. 061301

    Pith/arXiv arXiv 2020

  75. [76]

    Martin, T

    J. Martin, T. Papanikolaou, L. Pinol, V. Vennin, Metric preheating and radiative decay in single- field inflation, JCAP 05 (2020) 003.arXiv:2002.01820,doi:10.1088/1475-7516/2020/05/003

    Pith/arXiv arXiv 2020

  76. [77]

    Adshead, J

    P. Adshead, J. T. Giblin, R. Grutkoski, Z. J. Weiner, Gauge preheating with full general relativity, JCAP 03 (2024) 017.arXiv:2311.01504,doi:10.1088/1475-7516/2024/03/017

    Pith/arXiv arXiv 2024

  77. [78]

    Caravano, G

    A. Caravano, G. Franciolini, S. Renaux-Petel, Ultraslow-roll inflation on the lattice: Backreaction and nonlinear effects, Phys. Rev. D 111 (6) (2025) 063518.arXiv:2410.23942,doi:10.1103/ PhysRevD.111.063518

    Pith/arXiv arXiv 2025

  78. [79]

    Caravano, G

    A. Caravano, G. Franciolini, S. Renaux-Petel, Ultraslow-roll inflation on the lattice. II. Non- perturbative curvature perturbation, Phys. Rev. D 112 (8) (2025) 083508.arXiv:2506.11795, doi:10.1103/39qd-gdfm

    arXiv 2025

  79. [80]

    Cotner, A

    E. Cotner, A. Kusenko, M. Sasaki, V. Takhistov, Analytic Description of Primordial Black Hole Formation from Scalar Field Fragmentation, JCAP 10 (2019) 077.arXiv:1907.10613,doi:10. 1088/1475-7516/2019/10/077

    Pith/arXiv arXiv 2019

  80. [81]

    Martin, T

    J. Martin, T. Papanikolaou, V. Vennin, Primordial black holes from the preheating instability in single-field inflation, JCAP 01 (2020) 024.arXiv:1907.04236,doi:10.1088/1475-7516/2020/ 01/024

    Pith/arXiv arXiv 2020

Showing first 80 references.