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arxiv: 2605.16426 · v1 · pith:FUWVQUY2new · submitted 2026-05-14 · 🌌 astro-ph.CO · gr-qc

Expected redshift drift for tilted observers

Franco R. de Pedro , Gabriel R. Bengochea This is my paper

Pith reviewed 2026-05-20 20:41 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords redshift drifttilted observerspeculiar motion1+3 covariant formalismFLRW backgroundEinstein-de SitterLambdaCDMcosmological kinematics
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The pith

Redshift drift for tilted observers includes a directional correction from peculiar expansion, shear, and acceleration.

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

The paper calculates the redshift drift measured by observers who have nonzero peculiar motion relative to the cosmic expansion. It begins with the exact redshift expression in the tilted observer frame and derives the drift rate as the usual FLRW background term plus an anisotropic correction. This correction is expressed through the peculiar expansion, the projected shear, and the projected acceleration along the chosen line of sight. The authors first isolate the kinematic effect in an Einstein-de Sitter background and then repeat the calculation inside LambdaCDM to show how the same tilt terms modify the standard drift signal. Real observers always possess some peculiar velocity, so the result supplies a concrete template for interpreting future drift measurements that will necessarily be made from a moving frame.

Core claim

Starting from the exact redshift measured in the tilted frame, the corresponding drift is an FLRW background term plus a directional correction driven by the observer's peculiar kinematics, encoded through peculiar expansion, projected shear, and projected acceleration along the line of sight.

What carries the argument

The 1+3 covariant decomposition of the tilted observer's four-velocity, which supplies the peculiar kinematic scalars (expansion, shear, acceleration) that enter the drift correction.

If this is right

  • In an EdS universe the drift signal receives a purely kinematic anisotropic correction with no background acceleration term.
  • In LambdaCDM the same kinematic corrections deform the standard isotropic drift curve in a direction-dependent manner.
  • The correction vanishes for observers comoving with the background and grows with the amplitude of the peculiar velocity components along the line of sight.
  • Future drift surveys must therefore account for observer motion to avoid misinterpreting directional differences as new cosmological signals.

Where Pith is reading between the lines

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

  • If the predicted directional pattern is confirmed, it could provide an independent consistency check on measured peculiar velocities at low redshift.
  • The same formalism could be applied to test whether observed drift anomalies in specific directions are due to local kinematics rather than modified gravity.
  • Extending the calculation to mildly inhomogeneous backgrounds would quantify how much the tilt correction competes with actual inhomogeneity effects.
  • Observational programs targeting the drift signal should include sky-position metadata to allow post-processing removal of the predicted tilt term.

Load-bearing premise

The background spacetime is assumed to be exactly FLRW with the tilt treated as a pure kinematic effect inside the 1+3 formalism, without higher-order relativistic corrections or backreaction.

What would settle it

High-precision redshift-drift measurements in several independent sky directions that show no residual directional variation after subtracting the predicted peculiar-motion correction would falsify the claim that the tilt terms are the dominant anisotropic contribution.

Figures

Figures reproduced from arXiv: 2605.16426 by Franco R. de Pedro, Gabriel R. Bengochea.

Figure 1
Figure 1. Figure 1: Einstein–de Sitter redshift drift prediction with and without the CF4-normalized tilted correction. The [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ΛCDM prediction for the redshift drift after adding the same tilted correction. The left panel shows the [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
read the original abstract

Redshift drift is usually discussed for observers comoving with the cosmological background, but realistic observations are made by observers with nonzero peculiar motion. In this work, we calculate the expected redshift drift for tilted observers within the covariant \(1+3\) formalism. Starting from the exact redshift measured in the tilted frame, we derive the corresponding drift as an FLRW background term plus a directional correction driven by the observer's peculiar kinematics, encoded through peculiar expansion, projected shear, and projected acceleration along the line of sight. We analyse first an Einstein--de Sitter (EdS) background, which isolates the purely kinematic effect of tilt in the absence of background acceleration, and then extend the calculation to \(\Lambda\)CDM in order to quantify how the same anisotropic corrections deform the standard drift signal in the concordance model.

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

0 major / 2 minor

Summary. The paper claims to derive the redshift drift for tilted observers in cosmology. Starting from the exact redshift in the tilted frame within the 1+3 covariant formalism on an FLRW background, the drift is obtained as the standard background term plus directional corrections driven by peculiar expansion, projected shear, and projected acceleration. This is analyzed for Einstein-de Sitter and then for ΛCDM backgrounds.

Significance. If the derivation holds, it offers a covariant and parameter-free way to include the effects of observer peculiar motion in redshift drift predictions. This is valuable for interpreting data from future experiments aiming to measure redshift drift. The explicit inclusion of kinematic terms like shear and acceleration projections is a clear strength, allowing for directional dependence to be quantified in both EdS and ΛCDM models without additional relativistic corrections beyond the declared scope.

minor comments (2)
  1. The manuscript would benefit from a brief discussion in the introduction of how this work relates to previous studies on redshift drift in perturbed cosmologies.
  2. In the EdS section, the figures showing the drift signal could include a comparison to the untilted case to highlight the correction magnitude.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and for recommending minor revision. The referee's description accurately reflects the derivation of redshift drift for tilted observers, including the decomposition into the FLRW background term and the directional corrections from peculiar expansion, projected shear, and acceleration. We appreciate the recognition of the approach's relevance for future observations.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives the redshift drift for tilted observers by starting from the exact redshift in the tilted frame and applying the standard 1+3 covariant formalism on an assumed exact FLRW background, yielding the standard background term plus line-of-sight projections of peculiar expansion, shear, and acceleration. This is a direct kinematic calculation with no reduction of any load-bearing step to a fitted parameter, self-definition, or self-citation chain. The EdS-to-LambdaCDM extension is a straightforward specialization of the same expressions, and the background assumption is declared as the explicit scope rather than derived internally.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review based on abstract only; the work relies on standard cosmological assumptions without introducing new free parameters or entities in the summary provided.

axioms (2)
  • domain assumption The universe background is described by an FLRW metric (EdS or LambdaCDM)
    Used as the base model for isolating tilt effects and extending to concordance cosmology
  • domain assumption Covariant 1+3 formalism accurately encodes observer peculiar kinematics
    Central to deriving the directional corrections from expansion, shear, and acceleration

pith-pipeline@v0.9.0 · 5660 in / 1217 out tokens · 47201 ms · 2026-05-20T20:41:02.707882+00:00 · methodology

discussion (0)

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Works this paper leans on

60 extracted references · 60 canonical work pages · 28 internal anchors

  1. [1]

    G. F. R. Ellis, R. Maartens, and M. A. H. MacCallum,Relativistic Cosmology(Cambridge University Press, Cambridge, 2012)

    work page 2012

  2. [2]

    C. G. Tsagas, A. Challinor, and R. Maartens, Physics Reports465, 61 (2008), 0705.4397

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  3. [3]

    M. S. Turner, Ann. Rev. Nucl. Part. Sci.72, 1 (2022), 2201.04741

    work page arXiv 2022

  4. [4]

    Planck 2018 results. I. Overview and the cosmological legacy of Planck

    Y. Akrami et al. (Planck), Astronomy & Astrophysics641, A1 (2020), 1807.06205

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  5. [5]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanim et al. (Planck), Astronomy & Astrophysics641, A6 (2020), erratum: Astron. Astrophys. 652 (2021) C4., 1807.06209

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  6. [6]

    Lahav and A

    O. Lahav and A. R. Liddle,Cosmological parameters (2023), Review of Particle Physics 2024 (Particle Data Group), Chapter 25 (2024), revised August 2023; published 2024., 2403.15526, URLhttps://pdg.lbl.gov/2024/reviews/ rpp2024-rev-cosmological-parameters.pdf

    work page arXiv 2023

  7. [7]

    Cortˆ es, O

    M. Cortˆ es, O. Lahav, and A. R. Liddle (2026), 2602.13523

    work page arXiv 2026

  8. [8]

    B. D. Fields, K. A. Olive, T.-H. Yeh, and C. Young,Big bang nucleosynthesis, Review of Particle Physics 2024 (Parti- cle Data Group), Chapter 24 (2024), revised August 2023; published 2024., URLhttps://pdg.lbl.gov/2024/reviews/ rpp2024-rev-bbang-nucleosynthesis.pdf

    work page 2024

  9. [9]

    Challenges for $\Lambda$CDM: An update

    L. Perivolaropoulos and F. Skara, New Astronomy Reviews95, 101659 (2022), 2105.05208

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  10. [10]

    Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

    E. Abdalla et al., Journal of High Energy Astrophysics34, 49 (2022), 2203.06142

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  11. [11]

    Di Valentino, Universe8, 399 (2022)

    E. Di Valentino, Universe8, 399 (2022)

    work page 2022

  12. [12]

    A. G. Adame et al. (DESI), JCAP02, 021 (2025), 2404.03002

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  13. [13]

    A measurement of large-scale peculiar velocities of clusters of galaxies: results and cosmological implications

    A. Kashlinsky, F. Atrio-Barandela, D. Kocevski, and H. Ebeling, The Astrophysical Journal Letters686, L49 (2008), 0809.3734

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  14. [14]

    The Statistical Significance of the "Dark Flow"

    R. Keisler, Astrophysical Journal Letters707, L42 (2009), 0910.4233

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  15. [15]

    Planck Collaboration, Astronomy & Astrophysics561, A97 (2014), 1303.5090

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  16. [16]

    A new measurement of the bulk flow of X-ray luminous clusters of galaxies

    A. Kashlinsky, F. Atrio-Barandela, H. Ebeling, A. Edge, and D. Kocevski, Astrophysical Journal Letters712, L81 (2010), 0910.4958

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  17. [17]

    On the Statistical Significance of the Bulk Flow Measured by the PLANCK Satellite

    F. Atrio-Barandela, Astronomy & Astrophysics557, A116 (2013), 1303.6614. 16

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  18. [18]

    R. B. Tully, H. M. Courtois, A. E. Dolphin, J. R. Fisher, P. Heraudeau, B. A. Jacobs, I. D. Karachentsev, D. Makarov, L. Makarova, S. Mitronova, et al., The Astronomical Journal146, 86 (2013), 1307.7213

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  19. [19]

    R. B. Tully, H. M. Courtois, and J. G. Sorce, The Astronomical Journal152, 50 (2016), 1605.01765

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  20. [20]

    R. B. Tully, E. Kourkchi, H. M. Courtois, G. S. Anand, J. P. Blakeslee, D. Brout, T. de Jaeger, A. Dupuy, D. Guinet, C. Howlett, et al., The Astrophysical Journal944, 94 (2023), 2209.11238

    work page arXiv 2023

  21. [21]

    L. A. Campbell, J. R. Lucey, M. Colless, D. H. Jones, C. M. Springob, C. Magoulas, R. N. Proctor, J. R. Mould, M. A. Read, S. Brough, et al., Monthly Notices of the Royal Astronomical Society443, 1231 (2014), 1406.4867

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  22. [22]

    C. M. Springob, C. Magoulas, M. Colless, J. Mould, P. Erdogdu, D. H. Jones, J. R. Lucey, L. Campbell, and C. J. Fluke, Monthly Notices of the Royal Astronomical Society445, 2677 (2014), 1409.6161

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  23. [23]

    K. L. Masters, C. M. Springob, and J. P. Huchra, The Astronomical Journal135, 1738 (2008), 0711.4305

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  24. [24]

    T. Hong, L. Staveley-Smith, K. Masters, C. Springob, L. Macri, B. Koribalski, H. Jones, and T. Jarrett,The 2mass tully-fisher survey: Mapping the mass in the universe(2012), arXiv:1212.2090, 1212.2090

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  25. [25]

    T. Hong, L. Staveley-Smith, K. L. Masters, C. M. Springob, L. M. Macri, B. S. Koribalski, D. H. Jones, T. H. Jarrett, A. C. Crook, C. Howlett, et al., Monthly Notices of the Royal Astronomical Society487, 2061 (2019), 1905.08530

    work page internal anchor Pith review Pith/arXiv arXiv 2061

  26. [26]

    Watkins, H

    R. Watkins, H. A. Feldman, and M. J. Hudson, Monthly Notices of the Royal Astronomical Society392, 743 (2009)

    work page 2009

  27. [27]

    Watkins and H

    R. Watkins and H. A. Feldman, Monthly Notices of the Royal Astronomical Society447, 132 (2015)

    work page 2015

  28. [28]

    Watkins, T

    R. Watkins, T. Allen, C. J. Bradford, A. Ramon, A. Walker, H. A. Feldman, R. Cionitti, Y. Al-Shorman, E. Kourkchi, and R. B. Tully, Monthly Notices of the Royal Astronomical Society524, 1885 (2023), 2302.02028

    work page arXiv 2023

  29. [29]

    Watkins and H

    R. Watkins and H. A. Feldman (2025), preprint, 2512.03168

    work page arXiv 2025

  30. [30]

    Past´ en, S

    E. Past´ en, S. G´ alvez, and V. H. C´ ardenas, Physics of the Dark Universe43, 101385 (2024), 2301.11246

    work page arXiv 2024

  31. [31]

    Collins and G

    C. Collins and G. Ellis, Physics Reports56, 65 (1979), ISSN 0370-1573

    work page 1979

  32. [32]

    C. G. Tsagas, Monthly Notices of the Royal Astronomical Society405, 503 (2010), 0902.3232

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  33. [33]

    C. G. Tsagas, Physical Review D84, 063503 (2011), 1107.4045

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  34. [34]

    C. G. Tsagas, Monthly Notices of the Royal Astronomical Society: Letters426, L36 (2012)

    work page 2012

  35. [35]

    C. G. Tsagas and M. I. Kadiltzoglou, Physical Review D92, 043515 (2015), 1507.04266

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  36. [36]

    C. G. Tsagas, M. I. Kadiltzoglou, and K. Asvesta, Astrophys. Space Sci.366, 90 (2021), 2105.09267

    work page arXiv 2021

  37. [37]

    C. G. Tsagas, The European Physical Journal C82, 521 (2022), 2112.04313

    work page arXiv 2022

  38. [38]

    C. G. Tsagas, Astrophys. J.997, 25 (2026), 2404.16719

    work page arXiv 2026

  39. [39]

    E. P. Miliou and C. G. Tsagas, Phys. Rev. D110, 063540 (2024), 2404.19046

    work page arXiv 2024

  40. [40]

    C. G. Tsagas (2025), 2501.04680

    work page arXiv 2025

  41. [41]

    C. G. Tsagas, L. Perivolaropoulos, and K. Asvesta, Phys. Rept.1178, 1 (2026), 2510.05340

    work page arXiv 2026

  42. [42]

    Migkas, F

    K. Migkas, F. Pacaud, G. Schellenberger, J. Erler, N. T. Nguyen-Dang, T. H. Reiprich, M. E. Ramos-Ceja, and L. Lovisari, Astronomy & Astrophysics649, A151 (2021), 2103.13904

    work page arXiv 2021

  43. [43]

    Luongo, M

    O. Luongo, M. Muccino, E. ´O Colg´ ain, M. M. Sheikh-Jabbari, and L. Yin, Physical Review D105, 103510 (2022), 2108.13228

    work page arXiv 2022

  44. [44]

    N. J. Secrest, S. von Hausegger, M. Rameez, R. Mohayaee, S. Sarkar, and J. Colin, The Astrophysical Journal Letters 908, L51 (2021), 2009.14826

    work page arXiv 2021

  45. [45]

    Asvesta, L

    K. Asvesta, L. Kazantzidis, L. Perivolaropoulos, and C. G. Tsagas, Monthly Notices of the Royal Astronomical Society 513, 2394 (2022), 2202.00962

    work page arXiv 2022

  46. [46]

    A. Sah, M. Rameez, S. Sarkar, and C. G. Tsagas, Eur. Phys. J. C85, 596 (2025), 2411.10838

    work page arXiv 2025

  47. [47]

    Cosmological peculiar velocities in general relativity

    C. Clarkson and R. Maartens (2026), 2603.14511

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  48. [48]

    C. G. Tsagas (2026), 2603.28377

    work page arXiv 2026

  49. [49]

    Peculiar velocities in the $\Lambda$CDM universe

    E. Patliaka and C. G. Tsagas (2026), 2604.24974

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  50. [50]

    Sandage, The Astrophysical Journal136, 319 (1962)

    A. Sandage, The Astrophysical Journal136, 319 (1962)

    work page 1962

  51. [51]

    G. C. McVittie, Astrophys. J.136, 334 (1962)

    work page 1962

  52. [52]

    Direct Measurement of Cosmological Parameters from the Cosmic Deceleration of Extragalactic Objects

    A. Loeb, The Astrophysical Journal Letters499, L111 (1998), astro-ph/9802122

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  53. [53]

    The time evolution of cosmological redshift as a test of dark energy

    A. Balbi and C. Quercellini, Mon. Not. Roy. Astron. Soc.382, 1623 (2007), 0704.2350

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  54. [54]

    Haehnelt et al., Tech

    M. Haehnelt et al., Tech. Rep. E-TRE-IOA-573-0001, ESO / E-ELT Programme (2010), issue 1

    work page 2010

  55. [55]

    Liske, A

    J. Liske, A. Grazian, E. Vanzella, M. Dessauges-Zavadsky, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, P. Bonifacio, et al., The Messenger133, 10 (2008)

    work page 2008

  56. [56]

    Marconi et al., inGround-based and Airborne Instrumentation for Astronomy X(2024), vol

    A. Marconi et al., inGround-based and Airborne Instrumentation for Astronomy X(2024), vol. 13096 ofProc. SPIE, p. 1309613, 2407.14601

    work page arXiv 2024

  57. [57]

    G. F. R. Ellis and H. van Elst, NATO Sci. Ser. C541, 1 (1999), gr-qc/9812046

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  58. [58]

    Redshift Dipoles from Non-Geodesic Observer Congruences in Covariant Cosmology

    E. Past´ en (2026), 2603.20963

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  59. [59]

    C. G. Tsagas and M. I. Kadiltzoglou, Physical Review D88, 083501 (2013), 1306.6501

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  60. [60]

    Tzartinoglou and C

    A. Tzartinoglou and C. G. Tsagas, Eur. Phys. J. C84, 1061 (2024), 2405.17592

    work page arXiv 2024