pith. sign in

arxiv: 2411.11990 · v3 · submitted 2024-11-18 · 🌀 gr-qc · astro-ph.CO· astro-ph.GA· hep-ph

The need for a nonlocal expansion in general relativity

Marco Galoppo , Giorgio Torrieri This is my paper

Pith reviewed 2026-05-23 08:36 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COastro-ph.GAhep-ph
keywords general relativitypost-Newtonian approximationnonlocal effectsangular momentumeffective field theoryrotating bodiesspacetime curvaturegalaxies
0
0 comments X

The pith

The post-Newtonian approximation may fail for wide-extended rotating bodies even in weak fields and slow velocities due to nonlocal angular momentum spanning spacetime curvature.

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

The paper argues that the usual post-Newtonian expansion in general relativity breaks down for large rotating objects such as galaxies because their angular momentum extends across regions where spacetime curvature is significant. This breakdown occurs even when the gravitational fields are weak and velocities are small. The authors introduce a new dimensionless quantity designed to detect this failure and compute its value using known analytic solutions for rotating bodies together with data on galaxies, binary systems, and the Laniakea supercluster. If the argument holds, a different effective field theory for general relativity would be required to incorporate these nonlocal angular momentum contributions.

Core claim

Motivated by known facts about effective field theory and non-Abelian gauge theory, we argue that the post-Newtonian approximation might fail even in the limit of weak fields and small velocities for wide-extended rotating bodies, where angular momentum spans significant spacetime curvature. We construct a novel dimensionless quantity that samples this breakdown, and we evaluate it by means of existing analytical solutions of rotating extended bodies and observational data. We give estimates for galaxies and binary systems, as well as our home in the Cosmos, Laniakea. We thus propose that a novel effective field theory of general relativity might be needed to account for the onset of nonzero

What carries the argument

A novel dimensionless quantity constructed to sample the breakdown of the post-Newtonian approximation arising from nonlocal angular momentum effects in wide-extended rotating bodies.

If this is right

  • The post-Newtonian approximation fails for wide-extended rotating bodies even at weak fields and low velocities.
  • A new effective field theory of general relativity is required to capture nonlocal angular momentum effects.
  • Numerical estimates of the dimensionless quantity reach appreciable values for galaxies and binary systems.
  • The same quantity can be evaluated for the Laniakea supercluster using existing data.

Where Pith is reading between the lines

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

  • Models of galactic rotation that rely on the post-Newtonian expansion may need revision when angular momentum spans large distances.
  • Future high-precision observations of extended rotating systems could directly test whether the proposed breakdown occurs.
  • The analogy with gauge-theory nonlocal effects might suggest concrete ways to build the required effective theory.

Load-bearing premise

The constructed dimensionless quantity correctly identifies a genuine breakdown of the post-Newtonian expansion due to nonlocal angular momentum effects that cannot be captured by standard local higher-order terms.

What would settle it

A direct calculation or observation showing that the post-Newtonian series still converges accurately for a wide-extended rotating body in which the new dimensionless quantity reaches order one or larger.

read the original abstract

Motivated by known facts about effective field theory and non-Abelian gauge theory, we argue that the post-Newtonian approximation might fail even in the limit of weak fields and small velocities for wide-extended rotating bodies, where angular momentum spans significant spacetime curvature. We construct a novel dimensionless quantity that samples this breakdown, and we evaluate it by means of existing analytical solutions of rotating extended bodies and observational data. We give estimates for galaxies and binary systems, as well as our home in the Cosmos, Laniakea. We thus propose that a novel effective field theory of general relativity might be needed to account for the onset of nonlocal angular momentum effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that the post-Newtonian approximation in general relativity may fail even in the weak-field, slow-velocity limit for wide-extended rotating bodies where angular momentum spans significant spacetime curvature. Motivated by analogies to effective field theory and non-Abelian gauge theory, the authors construct a novel dimensionless quantity to diagnose this potential breakdown, evaluate it on existing analytical solutions of rotating bodies and observational data (including galaxies, binaries, and Laniakea), and propose that a new nonlocal effective field theory of GR is needed to capture nonlocal angular-momentum effects.

Significance. If the constructed quantity indeed isolates an irreducible nonlocal contribution outside the reach of any finite-order local post-Newtonian or post-Minkowskian expansion (including all curvature and spin couplings), the result would have substantial implications for the modeling of galactic dynamics, binary inspirals involving extended sources, and large-scale structure in GR. The concrete numerical estimates on known solutions and data constitute a strength, providing falsifiable targets. The work also highlights a possible gap in standard EFT approaches to GR, though its significance depends on establishing that the diagnostic cannot be reproduced by local higher-order terms.

major comments (2)
  1. [§3] §3 (construction of the dimensionless quantity): The quantity is motivated by the EFT/gauge-theory analogy and evaluated on solutions, but the manuscript provides no explicit derivation or term in the Einstein equations, geodesic deviation, or multipole expansion showing that the effect becomes non-perturbative or irreducible once the quantity is O(1); it therefore remains possible that the contribution lies within the span of local higher-order PN terms.
  2. [§4–5] §4–5 (evaluation on solutions and data): While the quantity reaches order-one values for some galaxies and binaries, the paper does not compare its magnitude against the known radius of convergence of the standard post-Newtonian series (including all local spin-curvature couplings) or demonstrate a concrete failure mode (e.g., a divergent coefficient or missing nonlocal kernel) that cannot be absorbed by existing local expansions.
minor comments (2)
  1. [Abstract] The abstract and introduction could more explicitly state whether the proposed nonlocal EFT modifies the Einstein-Hilbert action at the level of the field equations or only the effective description of sources.
  2. [§2] Notation for the dimensionless quantity and its relation to angular momentum and curvature scales should be introduced with a clear equation number early in the text for easier cross-reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (construction of the dimensionless quantity): The quantity is motivated by the EFT/gauge-theory analogy and evaluated on solutions, but the manuscript provides no explicit derivation or term in the Einstein equations, geodesic deviation, or multipole expansion showing that the effect becomes non-perturbative or irreducible once the quantity is O(1); it therefore remains possible that the contribution lies within the span of local higher-order PN terms.

    Authors: The dimensionless quantity is constructed as a diagnostic motivated by the scaling in EFT and non-Abelian gauge theory, where O(1) values of analogous ratios signal the onset of effects outside local perturbative expansions. We do not provide an explicit term in the Einstein equations because the manuscript focuses on identifying the regime rather than deriving the nonlocal correction; the quantity measures the ratio of angular-momentum extent to curvature radius in a manner that local derivative expansions (even at high order) are not guaranteed to reproduce if the underlying effect is nonlocal. We agree that showing explicit irreducibility would strengthen the argument and will add a clarifying paragraph in §3 emphasizing the diagnostic character and the scaling argument against absorption by local terms. revision: partial

  2. Referee: [§4–5] §4–5 (evaluation on solutions and data): While the quantity reaches order-one values for some galaxies and binaries, the paper does not compare its magnitude against the known radius of convergence of the standard post-Newtonian series (including all local spin-curvature couplings) or demonstrate a concrete failure mode (e.g., a divergent coefficient or missing nonlocal kernel) that cannot be absorbed by existing local expansions.

    Authors: The evaluations in §§4–5 show the quantity attaining O(1) values on concrete solutions and data, which we take as evidence that the regime of interest is physically realized. We have not performed an explicit comparison to the PN radius of convergence or isolated a divergent coefficient, as that would require a separate, more technical calculation. We will revise the discussion in §5 to reference existing literature on PN convergence limits and to state explicitly that the new quantity provides an independent indicator whose O(1) values motivate investigation of possible nonlocal kernels not captured by local expansions. revision: partial

Circularity Check

0 steps flagged

No circularity: construction and evaluation rely on external solutions and data

full rationale

The paper motivates a dimensionless quantity via EFT/gauge analogy, then evaluates that quantity on independent analytical solutions for rotating bodies and on observational data for galaxies, binaries, and Laniakea. No step reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or definitional tautology; the central proposal remains a suggestion rather than an output forced by the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard domain assumptions about the post-Newtonian expansion and analogies to EFT in other theories; the key ad hoc assumption is that angular momentum spanning curvature produces nonlocal effects requiring a new framework. No free parameters or invented entities are introduced beyond the diagnostic quantity itself.

axioms (2)
  • domain assumption The post-Newtonian approximation is the appropriate local expansion for weak fields and slow velocities in GR.
    Invoked as the baseline whose potential failure is being sampled.
  • ad hoc to paper Angular momentum spanning significant spacetime curvature produces nonlocal effects not captured by standard local expansions.
    This premise directly motivates the construction of the dimensionless quantity and the call for a new EFT.

pith-pipeline@v0.9.0 · 5636 in / 1564 out tokens · 50050 ms · 2026-05-23T08:36:00.192984+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

72 extracted references · 72 canonical work pages · 1 internal anchor

  1. [1]

    Will, On the unreasonable effectiveness of the post-newtonian approximation in gravitational physics, PNAS 108 (2011) 5938–5945

    C.M. Will, On the unreasonable effectiveness of the post-newtonian approximation in gravitational physics, PNAS 108 (2011) 5938–5945

    work page 2011

  2. [2]

    Will, The confrontation between general relativity and experiment , Liv

    C. Will, The confrontation between general relativity and experiment , Liv. Rev. Rel. 17 (2014) 4

    work page 2014

  3. [3]

    Poisson and C.M

    E. Poisson and C.M. Will, Gravity, Newtonian, Post-Newtonian, Relativistic , Cambridge University Press (2014), 10.1017/CBO9781139507486

    work page doi:10.1017/cbo9781139507486 2014

  4. [4]

    Bertone, D

    G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and constraints , Phys. Rept. 405 (2005) 279

    work page 2005

  5. [5]

    Bekenstein, Relativistic gravitation theory for the mond paradigm , Phys

    J.D. Bekenstein, Relativistic gravitation theory for the mond paradigm , Phys. Rev. D 70 (2004) 083509

    work page 2004

  6. [6]

    Rubin, J

    V.C. Rubin, J. Ford, W. K. and N. Thonnard, Extended rotation curves of high-luminosity spiral galaxies. IV. Systematic dynamical properties, Sa -¿ Sc. , Astrophys. J. Lett. 225 (1978) L107

    work page 1978

  7. [7]

    Bosma, The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types., Ph.D

    A. Bosma, The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types., Ph.D. thesis, Groningen Univ., Groningen, The Netherlands, 1978

    work page 1978

  8. [8]

    Sofue and V

    Y. Sofue and V. Rubin, Rotation Curves of Spiral Galaxies , Ann. Rev. Astron. Astrophys. 39 (2001) 137

    work page 2001

  9. [9]

    Treu, Strong Lensing by Galaxies , ARA&A 48 (2010) 87

    T. Treu, Strong Lensing by Galaxies , ARA&A 48 (2010) 87. – 10 –

    work page 2010

  10. [10]

    Bartelmann, TOPICAL REVIEW Gravitational lensing , Class

    M. Bartelmann, TOPICAL REVIEW Gravitational lensing , Class. Quantum Grav. 27 (2010) 233001

    work page 2010

  11. [11]

    Del Popolo, Dark matter, density perturbations, and structure formation

    A. Del Popolo, Dark matter, density perturbations, and structure formation. , Astron. Rept. 51 (2007) 169

    work page 2007

  12. [12]

    Cooperstock and S

    F.I. Cooperstock and S. Tieu, Galactic Dynamics via General Relativity: A Compilation and New Developments, Int. J. Mod. Phys. A 22 (2007) 2293

    work page 2007

  13. [13]

    Balasin and D

    H. Balasin and D. Grumiller, Non-newtonian behavior in weak field general relativity for extended rotating sources, Int. J. Mod. Phys. D 17 (2008) 475

    work page 2008

  14. [14]

    Astesiano, S.L

    D. Astesiano, S.L. Cacciatori, V. Gorini and F. Re, Towards a full general relativistic approach to galaxies, Eur. Phys. J. C 82 (2022) 554

    work page 2022

  15. [15]

    Astesiano and M.L

    D. Astesiano and M.L. Ruggiero, Galactic dark matter effects from purely geometrical aspects of general relativity, Phys. Rev. D 106 (2022) 044061

    work page 2022

  16. [16]

    Ruggiero, Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects, J

    M.L. Ruggiero, Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects, J. Cosmol. Astropart. Phys. 02 (2024) 025

    work page 2024

  17. [17]

    Re and M

    F. Re and M. Galoppo, Effective galactic dark matter: first order general relativistic corrections, Class. Quantum Grav. 42 (2025) in press

    work page 2025

  18. [18]

    Galoppo, F

    M. Galoppo, F. Re and D.L. Wiltshire, Quasilocal newtonian limit of galactic dynamics in general relativity, arXiv:2408.00358 (2024)

    work page arXiv 2024

  19. [19]

    Rowland, On claims that general relativity differs from newtonian physics for self-gravitating dusts in the low velocity, weak field limit , Int

    D.R. Rowland, On claims that general relativity differs from newtonian physics for self-gravitating dusts in the low velocity, weak field limit , Int. J. Mod. Phys. D 24 (2015) 1550065

    work page 2015

  20. [20]

    Ciotti, On the rotation curve of disk galaxies in General Relativity , Astrophys

    L. Ciotti, On the rotation curve of disk galaxies in General Relativity , Astrophys. J. 936 (2022) 180

    work page 2022

  21. [21]

    Lasenby, M.P

    A.N. Lasenby, M.P. Hobson and W.E.V. Barker, Gravitomagnetism and galaxy rotation curves: a cautionary tale , Class. Quantum Grav. 40 (2023) 215014

    work page 2023

  22. [22]

    Costa and J

    L.F.O. Costa and J. Nat´ ario,Relativistic effects cannot explain galactic dynamics , Phys. Rev. D 110 (2024) 064056

    work page 2024

  23. [23]

    Porto, The effective field theorist’s approach to gravitational dynamics , Phys

    R.A. Porto, The effective field theorist’s approach to gravitational dynamics , Phys. Rep. 633 (2016) 1

    work page 2016

  24. [24]

    Notari, Late time failure of Friedmann equation , Mod

    A. Notari, Late time failure of Friedmann equation , Mod. Phys. Lett. A 21 (2006) 2997

    work page 2006

  25. [25]

    Wiltshire, Cosmic clocks, cosmic variance and cosmic averages , New J

    D.L. Wiltshire, Cosmic clocks, cosmic variance and cosmic averages , New J. Phys. 9 (2007) 377

    work page 2007

  26. [26]

    Wiltshire, Cosmological equivalence principle and the weak-field limit , Phys

    D.L. Wiltshire, Cosmological equivalence principle and the weak-field limit , Phys. Rev. D 78 (2008) 084032

    work page 2008

  27. [27]

    Buchert and S

    T. Buchert and S. R¨ as¨ anen,Backreaction in late-time cosmology, Ann. Rev. Nucl. Part. Sci. 62 (2012) 57

    work page 2012

  28. [28]

    When Effective Field Theories Fail

    J.F. Donoghue, When effective field theories fail , arXiv:0909.0021 (2009)

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  29. [29]

    Goldstein, C

    H. Goldstein, C. Poole and J. Safko, Classical Mechanics (3rd ed.), Addison-Wesley (2002)

    work page 2002

  30. [30]

    Mouhot and C

    C. Mouhot and C. Villani, On Landau damping , Acta Mathematica 207 (2011) 29

    work page 2011

  31. [31]

    Peskin and D.V

    M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory , Addison-Wesley (1995), 0.1201/9780429503559

    work page 1995

  32. [32]

    Gribov, Quantization of non-abelian gauge theories , Nucl

    V. Gribov, Quantization of non-abelian gauge theories , Nucl. Phys. B 139 (1978) 1. – 11 –

    work page 1978

  33. [33]

    Dudal, J.A

    D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel and H. Verschelde, Refinement of the gribov-zwanziger approach in the landau gauge: Infrared propagators in harmony with the lattice results, Phys. Rev. D 78 (2008) 065047

    work page 2008

  34. [34]

    Pisarski, Effective theory of wilson lines and deconfinement , Phys

    R.D. Pisarski, Effective theory of wilson lines and deconfinement , Phys. Rev. D 74 (2006) 121703

    work page 2006

  35. [35]

    Brambilla, A

    N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: An Effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275

    work page 2000

  36. [36]

    Linde, Infrared Problem in Thermodynamics of the Yang-Mills Gas , Phys

    A.D. Linde, Infrared Problem in Thermodynamics of the Yang-Mills Gas , Phys. Lett. B 96 (1980) 289

    work page 1980

  37. [37]

    Arnold, Quark-Gluon Plasmas and Thermalization , Int

    P.B. Arnold, Quark-Gluon Plasmas and Thermalization , Int. J. Mod. Phys. E 16 (2007) 2555

    work page 2007

  38. [38]

    Majumder, Calculating the jet quenching parameter ˆq in lattice gauge theory , Phys

    A. Majumder, Calculating the jet quenching parameter ˆq in lattice gauge theory , Phys. Rev. C 87 (2013) 034905

    work page 2013

  39. [39]

    Deur, Implications of graviton-graviton interaction to dark matter , Phys

    A. Deur, Implications of graviton-graviton interaction to dark matter , Phys. Lett. B 676 (2009) 21

    work page 2009

  40. [40]

    Avery and B.U.W

    S.G. Avery and B.U.W. Schwab, Noether’s second theorem and ward identities for gauge symmetries, J. High Energ. Phys. 2016 (2016) 31

    work page 2016

  41. [41]

    Penrose, Quasilocal mass and angular momentum in general relativity , Proc

    R. Penrose, Quasilocal mass and angular momentum in general relativity , Proc. Roy. Soc. Lond. A 381 (1982) 53–63

    work page 1982

  42. [42]

    Bluman and S

    G. Bluman and S. Kumei, Symmetries and Differential Equations , Applied Mathematical Sciences, Springer New York (2013)

    work page 2013

  43. [44]

    Synge, Relativity: The General Theory , North Holland (1960)

    J.L. Synge, Relativity: The General Theory , North Holland (1960)

    work page 1960

  44. [45]

    Poisson, A

    E. Poisson, A. Pound and I. Vega, The motion of point particles in curved spacetime , Living Rev. Relativ. 14 (2011)

    work page 2011

  45. [46]

    Mourier and A

    P. Mourier and A. Heinesen, Splitting the spacetime: a systematic analysis of foliation dependence in cosmic averaging, J. Cosmol. Astropart. Phys. 2024 (2024) 067

    work page 2024

  46. [47]

    Jackiw, V.P

    R. Jackiw, V.P. Nair, S.-Y. Pi and A.P. Polychronakos, Perfect fluid theory and its extensions , J. Phys. A: Math. Gen. 37 (2004) R327

    work page 2004

  47. [48]

    Dubovsky, T

    S. Dubovsky, T. Gr´ egoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, J. High Energ. Phys. 2006 (2006) 025

    work page 2006

  48. [49]

    Lynden-Bell, Statistical Mechanics of Violent Relaxation in Stellar Systems , Mon

    D. Lynden-Bell, Statistical Mechanics of Violent Relaxation in Stellar Systems , Mon. Not. R. Astron. Soc. 136 (1967) 101–121

    work page 1967

  49. [50]

    Schutz, A First Course in General Relativity , Cambridge University Press (1985), 10.1017/CBO9780511984181

    B.F. Schutz, A First Course in General Relativity , Cambridge University Press (1985), 10.1017/CBO9780511984181

    work page doi:10.1017/cbo9780511984181 1985

  50. [51]

    Goodstein, States of Matter , Dover Books on Physics, Dover Publications (1985)

    D. Goodstein, States of Matter , Dover Books on Physics, Dover Publications (1985)

    work page 1985

  51. [52]

    Wilson, Confinement of quarks , Phys

    K.G. Wilson, Confinement of quarks , Phys. Rev. D 10 (1974) 2445

    work page 1974

  52. [53]

    Greensite, An introduction to the confinement problem , Springer (2011), 10.1007/978-3-642-14382-3

    J. Greensite, An introduction to the confinement problem , Springer (2011), 10.1007/978-3-642-14382-3

    work page doi:10.1007/978-3-642-14382-3 2011

  53. [54]

    White, Factorization Properties of Soft Graviton Amplitudes , J

    C.D. White, Factorization Properties of Soft Graviton Amplitudes , J. High Energ. Phys. 05 (2011) 060

    work page 2011

  54. [55]

    Bonocore, A

    D. Bonocore, A. Kulesza and J. Pirsch, Classical and quantum gravitational scattering with Generalized Wilson Lines, J. High Energ. Phys. 03 (2022) 147. – 12 –

    work page 2022

  55. [56]

    Wiegert and M.J

    P.A. Wiegert and M.J. Holman, The Stability of Planets in the Alpha Centauri System , Astrophys. J. 113 (1997) 1445

    work page 1997

  56. [57]

    Taylor and J.M

    J.H. Taylor and J.M. Weisberg, A new test of general relativity - Gravitational radiation and the binary pulsar PSR 1913+16 , Astrophys. J. 253 (1982) 908

    work page 1913

  57. [58]

    Tully et al., The Laniakea supercluster of galaxies , Nature 513 (2014) 71

    R.B. Tully et al., The Laniakea supercluster of galaxies , Nature 513 (2014) 71

    work page 2014

  58. [59]

    Valade et al., Identification of basins of attraction in the local Universe , Nat

    A. Valade et al., Identification of basins of attraction in the local Universe , Nat. Astron. 78 (2024) 084032

    work page 2024

  59. [60]

    Plummer, On the problem of distribution in globular star clusters , Mon

    H.C. Plummer, On the problem of distribution in globular star clusters , Mon. Not. R. Astron. Soc. 71 (1911) 460

    work page 1911

  60. [61]

    Binney and S

    J. Binney and S. Tremaine, Galactic Dynamics: Second Edition , Princeton University Press (2008), 10.2307/j.ctvc778ff

    work page doi:10.2307/j.ctvc778ff 2008

  61. [62]

    Kuzmin, Constraining the nfw potential with observations and modeling of low surface brightness galaxy velocity fields , Astron

    G.G. Kuzmin, Constraining the nfw potential with observations and modeling of low surface brightness galaxy velocity fields , Astron. Zh. 33 (1956)

    work page 1956

  62. [63]

    Dupuy and H.M

    A. Dupuy and H.M. Courtois, Dynamic cosmography of the local Universe: Laniakea and five more watershed superclusters, Astron. Astrophys. 678 (2023) A176

    work page 2023

  63. [64]

    Courtois et al., Gravity in the local Universe: Density and velocity fields using CosmicFlows-4, Astron

    H.M. Courtois et al., Gravity in the local Universe: Density and velocity fields using CosmicFlows-4, Astron. Astrophys. 670 (2023) L15

    work page 2023

  64. [65]

    Tully et al., Cosmicflows-4, Astrophys

    R.B. Tully et al., Cosmicflows-4, Astrophys. J. 944 (2023) 94

    work page 2023

  65. [66]

    Giani, C

    L. Giani, C. Howlett, K. Said, T. Davis and S. Vagnozzi, An effective description of laniakea: impact on cosmology and the local determination of the hubble constant , J. Cosmol. Astropart. Phys. 2024 (2024) 071

    work page 2024

  66. [67]

    Clowe, A

    D. Clowe, A. Gonzalez and M. Markevitch, Weak lensing mass reconstruction of the interacting cluster 1E0657-558: Direct evidence for the existence of dark matter , Astrophys. J. 604 (2004) 596

    work page 2004

  67. [68]

    Simon, The Faintest Dwarf Galaxies , ARA&A 57 (2019) 375

    J.D. Simon, The Faintest Dwarf Galaxies , ARA&A 57 (2019) 375

    work page 2019

  68. [69]

    Planck collaboration, Planck 2015 results. XIII. Cosmological parameters , Astron. Astrophys. 594 (2016) A13

    work page 2015

  69. [70]

    Matarrese, S

    S. Matarrese, S. Mollerach, A. Notari and A. Riotto, Large-scale magnetic fields from density perturbations, Phys. Rev. D 71 (2005) 043502

    work page 2005

  70. [71]

    Durrer and A

    R. Durrer and A. Neronov, Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev. 21 (2013) 62

    work page 2013

  71. [72]

    Bruni, D.B

    M. Bruni, D.B. Thomas and D. Wands, Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach , Phys. Rev. D 89 (2014) 044010

    work page 2014

  72. [73]

    Thomas, M

    D.B. Thomas, M. Bruni and D. Wands, The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations , Mon. Not. R. Astron. Soc. 452 (2015) 1727. – 13 –

    work page 2015