Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory

Basheer Kalbouneh; Chris Clarkson; Christian Marinoni; Maharshi Sarma; Roy Maartens

Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory

T0 review · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Off-center observers in a spherical LTB overdensity get accurate cosmographic distances up to δc≈2.5 near the structure, while linear perturbation theory is better beyond ~3Rs; a gauge dictionary links the two.

desk verdict Solid analytic machinery and a useful gauge dictionary, but the headline accuracy thresholds are over-generalized from a single density profile. read the letter →

arxiv 2510.03517 v2 pith:KQZIZC4C submitted 2025-10-03 astro-ph.CO gr-qc

Maharshi Sarma , Christian Marinoni , Basheer Kalbouneh , Chris Clarkson , Roy Maartens This is my paper · ORCID

classification astro-ph.COgr-qc

keywords anisotropiescovariantlocalanalysisapproachcomparecosmographicdistance

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

The paper studies a toy universe called an LTB model: spherically symmetric, with one dense clump in an otherwise smooth expanding background. An observer sits off to one side of this clump. The authors compute the true distance to galaxies by tracing light rays through the curved spacetime using the Sachs equation. They then compare this exact answer with two low-cost approximations: a Taylor-series 'covariant cosmography' expansion of distance in redshift, and linear perturbation theory around a smooth universe.

They find that near the clump, cosmography with terms through jerk and curvature stays within about 10 percent error up to a central overdensity of about 2.5 times the background density, while perturbation theory already fails at overdensity about 1. Far from the clump, perturbation theory wins: it stays accurate for overdensities up to about 3, while cosmography errors climb above 10 percent beyond central contrasts of about 1.5. They also derive a dictionary connecting the LTB language to the perturbed-FLRW language, resolving a mismatch in the monopole of the Hubble parameter as a gauge artifact, and correcting a typo in an earlier paper's quadrupole formula.

The main caveat: all thresholds come from one analytic density profile and one fixed size parameter; the generalized statements in the abstract assume this profile is representative.

Extended reading notes

Core claim

For a spherical overdensity, linear perturbation theory already exceeds 10% error in the luminosity distance toward the center for δc ≳ 1 when the observer lies within the typical size of the structure. In contrast, cosmographic reconstruction maintains better than 10% accuracy up to δc ≲ 2.5. At larger radii the situation reverses: LPT remains accurate up to δc ≲ 3, while CC already exceeds 10% error for δc ≳ 1.5. (Abstract and Conclusions.)

Load-bearing premise

The quantitative 10%-accuracy thresholds are computed for a single analytic density profile, Eq. (4.2), with the shape parameter fixed and Rs held at 37.4 Mpc throughout the parameter scans in Figure 6. The abstract and conclusions generalize these thresholds to 'a spherical overdensity' without testing profile-shape dependence, multiple structures, or nonzero Λ. If other realistic profiles shift the boundaries, the load-bearing regime statements would not hold as stated.

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Desk Editor's Note

read the letter

Useful paper, with a real caveat. The genuinely new content is the analytic multipole expressions for the covariant cosmographic parameters for an off-center LTB observer, the exact-vs-approximate error map against the Sachs-equation distance, and a careful gauge dictionary between linearized LTB and LPT in Newtonian gauge. The dictionary is the strongest part—it resolves the H0 monopole mismatch with the earlier paper [43] and corrects the H2 formula, which is the kind of detail that earns trust. The comparison is not circular: the CC coefficients come from metric derivatives, not from fitting the exact distance.

The soft spot is exactly what the stress-test flags: the 10% regime boundaries in Figures 6/7 come from one density profile, Eq. (4.2), with the shape exponent fixed and Rs = 37.4 Mpc throughout the parameter scans, and with Λ = 0. That profile is an uncompensated power-law whose enclosed mass excess diverges logarithmically; a compact or compensated profile could plausibly shift the convergence radii. The abstract then states the thresholds for 'a spherical overdensity' without qualification. The paper's own §6 admits the practical fitting procedure lowers the theoretical error further, so the reported numbers are model- and estimator-dependent. This does not sink the paper—the qualitative conclusion (CC wins near dense regions, LPT at larger separations) is plausible and the methodology is sound—but the abstract overclaims.

Minor points: no code or numerical convergence tests are shown, and 'LPT' here is really linear perturbation theory in Newtonian gauge, not standard Lagrangian PT. The derivation chain is long and dense; the appendices help.

Who this is for: applied cosmologists interpreting expansion-rate anisotropies and anyone using covariant cosmography in the local universe. It deserves a serious referee. I would ask the authors to narrow the conclusions to the tested profile family, or add a robustness check with a compact or compensated profile (or nonzero Λ). The referee should focus on whether the thresholds survive that test.

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

The central claims rest on general relativity, standard Sachs optics, and a specific ad hoc density profile. No new particles, forces, or geometric entities are introduced; the only adjustable inputs are the model parameters δc, Rs, χo, and H∞.

free parameters (4)

δc = 2.5 (model M1); -0.22 illustrative H0 example
Central density contrast of the profile (4.2), chosen by hand; drives the nonlinearity and the reported thresholds.
Rs = 37.4 Mpc
Characteristic radius of the density profile, taken from model M1 of [43]; kept fixed in parameter scans.
χo = 200 Mpc (≈5.35 Rs) in fiducial runs, varied in scans
Observer distance from the center of the inhomogeneity; controls the reported regimes.
H∞ = 70 km/s/Mpc
Asymptotic EdS expansion rate used to set t0 and normalize the background; a chosen input rather than a fitted constant.

assumptions (5)

domain assumption Gravity is described by general relativity with pressureless dust and Λ=0 in the LTB model.
The entire LTB construction and the comparison with EdS background rely on this; stated in §2.
standard math The angular diameter distance is given by the Sachs equation with the optical tidal tensor of Eq. (A.23).
The exact distance used as ground truth in §4 is computed from this standard geodesic-deviation framework, derived in Appendix A.
ad hoc to paper The matter profile is the specific analytic form δ(χ)=δc(1+(χ/Rs)^2)^(-3/2) asymptoting to EdS.
Eq. (4.2). All quantitative reliability claims depend on this shape; no other profile shapes are tested.
domain assumption The LTB metric can be linearized around an EdS background with |δa/a|≪1 and |k|≪1.
Eqs. (5.21)–(5.22). This is the basis of the linearized-LTB dictionary and the LPT comparison.
domain assumption In the Newtonian gauge the perturbations have no anisotropic stress (Ψ=Φ), a time-independent potential, and a growing-mode velocity field with the integration constant C2=0.
§5.2, Eqs. (5.32)–(5.41). These assumptions are needed to derive the dictionary and the Hubble-monopole gauge correction.

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Pith. "Pith review of Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory." pith.science (2026). https://pith.science/paper/KQZIZC4C

@misc{pith2026251003517,
  author       = {Pith},
  title        = {Pith review of: Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KQZIZC4C}},
  note         = {Machine review of arXiv:2510.03517}
}

read the original abstract

Recent observational evidence of axially symmetric anisotropies in the local cosmic expansion rate motivates an investigation of whether they can be accounted for within the Lema\^itre-Tolman-Bondi (LTB) framework with an off-center observer. Within this setting, we compute the exact relativistic luminosity distance via the Sachs equation and compare it with the approximate expression obtained from the covariant cosmographic approach (including Hubble, deceleration, jerk and curvature parameters). This comparison allows us to identify the regimes in which the covariant cosmographic method remains reliable. In addition, we compare the LTB relativistic distance for small inhomogeneities with the corresponding result derived from linear perturbation theory (LPT) in the standard cosmological model. This analysis establishes a precise correspondence between the LTB and LPT approaches, offering a consistent dictionary for the interpretation of the observed anisotropies of the large-scale gravitational field. This analysis will be instrumental in interpreting expansion-rate anisotropies, facilitating investigations of the local Universe beyond the FLRW framework with a fully non-perturbative metric approach.

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Works this paper leans on

61 extracted references · 47 linked inside Pith · cited by 1 Pith paper

[43]

Kalbouneh, C

B. Kalbouneh, C. Marinoni and R. Maartens,Cosmography of the local Universe by multipole analysis of the expansion rate fluctuation field,JCAP09(2024) 069 [2401.12291]

arXiv 2024
[1]

Di Valentino, O

E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri et al.,In the realm of the Hubble tension—a review of solutions,Class. Quant. Grav.38(2021) 153001 [2103.01183]

arXiv 2021
[2]

Perivolaropoulos and F

L. Perivolaropoulos and F. Skara,Challenges forΛCDM: An update,New Astron. Rev.95(2022) 101659 [2105.05208]

arXiv 2022
[3]

Schöneberg, G

N. Schöneberg, G. Franco Abellán, A. Pérez Sánchez, S.J. Witte, V . Poulin and J. Lesgourgues,The H0 Olympics: A fair ranking of proposed models,Phys. Rept.984(2022) 1 [2107.10291]

arXiv 2022
[4]

E. Abdalla et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,JHEAp34(2022) 49 [2203.06142]

arXiv 2022
[5]

Capozziello, G

S. Capozziello, G. Sarracino and G. De Somma,A Critical Discussion on the H 0 Tension †,Universe10 (2024) 140 [2403.12796]. – 32 –

arXiv 2024
[6]

Bengaly, J.S

C.A.P. Bengaly, J.S. Alcaniz and C. Pigozzo,Testing the isotropy of cosmic acceleration with the Pantheon+and SH0ES datasets: A cosmographic analysis,Phys. Rev. D109(2024) 123533 [2402.17741]

arXiv 2024
[7]

Schwarz and B

D.J. Schwarz and B. Weinhorst,(An)isotropy of the Hubble diagram: Comparing hemispheres,Astron. Astrophys.474(2007) 717 [0706.0165]

arXiv 2007

Show all 61 references

[8]

Kashlinsky, F

A. Kashlinsky, F. Atrio-Barandela, D. Kocevski and H. Ebeling,A measurement of large-scale peculiar velocities of clusters of galaxies: results and cosmological implications,Astrophys. J. Lett.686(2009) L49 [0809.3734]

2009 arXiv
[9]

Antoniou and L

I. Antoniou and L. Perivolaropoulos,Searching for a Cosmological Preferred Axis: Union2 Data Analysis and Comparison with Other Probes,JCAP12(2010) 012 [1007.4347]

2010 arXiv
[10]

Cai and Z.-L

R.-G. Cai and Z.-L. Tuo,Direction Dependence of the Deceleration Parameter,JCAP02(2012) 004 [1109.0941]

2012 arXiv
[11]

Marinoni, J

C. Marinoni, J. Bel and A. Buzzi,The Scale of Cosmic Isotropy,JCAP10(2012) 036 [1205.3309]

2012 arXiv
[12]

Kalus, D.J

B. Kalus, D.J. Schwarz, M. Seikel and A. Wiegand,Constraints on anisotropic cosmic expansion from supernovae,Astron. Astrophys.553(2013) A56 [1212.3691]

2013 arXiv
[13]

Wang and F.Y

J.S. Wang and F.Y . Wang,Probing the anisotropic expansion from supernovae and GRBs in a model-independent way,Mon. Not. Roy. Astron. Soc.443(2014) 1680 [1406.6448]

2014 arXiv
[14]

M. Yoon, D. Huterer, C. Gibelyou, A. Kovács and I. Szapudi,Dipolar modulation in number counts of WISE-2MASS sources,Mon. Not. Roy. Astron. Soc.445(2014) L60 [1406.1187]

2014 arXiv
[15]

Tiwari and A

P. Tiwari and A. Nusser,Revisiting the NVSS number count dipole,JCAP03(2016) 062 [1509.02532]

2016 arXiv
[16]

Javanmardi, C

B. Javanmardi, C. Porciani, P. Kroupa and J. Pflamm-Altenburg,Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae,Astrophys. J.810(2015) 47 [1507.07560]

2015 arXiv
[17]

Bengaly, Jr.,Constraining the local variance of H 0 from directional analyses,JCAP04(2016) 036 [1510.05545]

C.A.P. Bengaly, Jr.,Constraining the local variance of H 0 from directional analyses,JCAP04(2016) 036 [1510.05545]

2016 arXiv
[18]

Colin, R

J. Colin, R. Mohayaee, M. Rameez and S. Sarkar,High redshift radio galaxies and divergence from the CMB dipole,Mon. Not. Roy. Astron. Soc.471(2017) 1045 [1703.09376]

2017 arXiv
[19]

Rameez, R

M. Rameez, R. Mohayaee, S. Sarkar and J. Colin,The dipole anisotropy of AllWISE galaxies,Mon. Not. Roy. Astron. Soc.477(2018) 1772 [1712.03444]

2018 arXiv
[20]

Migkas, G

K. Migkas, G. Schellenberger, T.H. Reiprich, F. Pacaud, M.E. Ramos-Ceja and L. Lovisari,Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX−T scaling relation,Astron. Astrophys.636(2020) A15 [2004.03305]

2020 arXiv
[21]

Migkas, F

K. Migkas, F. Pacaud, G. Schellenberger, J. Erler, N.T. Nguyen-Dang, T.H. Reiprich et al., Cosmological implications of the anisotropy of ten galaxy cluster scaling relations,Astron. Astrophys. 649(2021) A151 [2103.13904]

2021 arXiv
[22]

Secrest, S

N.J. Secrest, S. von Hausegger, M. Rameez, R. Mohayaee, S. Sarkar and J. Colin,A Test of the Cosmological Principle with Quasars,Astrophys. J. Lett.908(2021) L51 [2009.14826]

2021 arXiv
[23]

Siewert, M

T.M. Siewert, M. Schmidt-Rubart and D.J. Schwarz,Cosmic radio dipole: Estimators and frequency dependence,Astron. Astrophys.653(2021) A9 [2010.08366]

2021 arXiv
[24]

Luongo, M

O. Luongo, M. Muccino, E.O. Colgáin, M.M. Sheikh-Jabbari and L. Yin,Larger H0 values in the CMB dipole direction,Phys. Rev. D105(2022) 103510 [2108.13228]

2022 arXiv
[25]

Krishnan, R

C. Krishnan, R. Mohayaee, E.O. Colgáin, M.M. Sheikh-Jabbari and L. Yin,Hints of FLRW breakdown from supernovae,Phys. Rev. D105(2022) 063514 [2106.02532]

2022 arXiv
[26]

Sorrenti, R

F. Sorrenti, R. Durrer and M. Kunz,The dipole of the Pantheon+SH0ES data,JCAP11(2023) 054 [2212.10328]. – 33 –

2023 arXiv
[27]

Aluri et al.,Is the observable Universe consistent with the cosmological principle?,Class

P.K. Aluri et al.,Is the observable Universe consistent with the cosmological principle?,Class. Quant. Grav.40(2023) 094001 [2207.05765]

2023 arXiv
[28]

Cowell, S

J.A. Cowell, S. Dhawan and H.J. Macpherson,Potential signature of a quadrupolar hubble expansion in Pantheon+supernovae,Mon. Not. Roy. Astron. Soc.526(2023) 1482 [2212.13569]

2023 arXiv
[29]

Hu, Y .Y

J.P. Hu, Y .Y . Wang, J. Hu and F.Y . Wang,Testing the cosmological principle with the Pantheon+sample and the region-fitting method,2310.11727

arXiv
[30]

Hu and F.-Y

J.-P. Hu and F.-Y . Wang,Hubble Tension: The Evidence of New Physics,Universe9(2023) 94 [2302.05709]

2023 arXiv
[31]

Dainotti, B

M.G. Dainotti, B. De Simone, T. Schiavone, G. Montani, E. Rinaldi and G. Lambiase,On the Hubble constant tension in the SNe Ia Pantheon sample,Astrophys. J.912(2021) 150 [2103.02117]

2021 arXiv
[32]

Dark Univ.49(2025) 101965 [2504.01669]

CosmoVerseNetworkcollaboration,The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics,Phys. Dark Univ.49(2025) 101965 [2504.01669]

2025 arXiv
[33]

Mazurenko, I

S. Mazurenko, I. Banik and P. Kroupa,The redshift dependence of the inferred H0 in a local void solution to the Hubble tension,Mon. Not. Roy. Astron. Soc.536(2025) 3232 [2412.12245]

2025 arXiv
[34]

A. Sah, M. Rameez, S. Sarkar and C.G. Tsagas,Anisotropy in Pantheon+supernovae,Eur. Phys. J. C 85(2025) 596 [2411.10838]

2025 arXiv
[35]

J.P. Hu, X.D. Jia, J. Hu and F.Y . Wang,Hints of New Physics for the Hubble Tension: Violation of Cosmological Principle,Astrophys. J. Lett.975(2024) L36 [2410.06450]

2024 arXiv
[36]

Franco, J

C. Franco, J. Oliveira, M. Lopes, F. Avila and A. Bernui,Measuring the matter fluctuations in the Local Universe with the ALFALFA catalogue,Mon. Not. Roy. Astron. Soc.537(2025) 897 [2406.16693]

2025 arXiv
[37]

J. Adam, R. Maartens, J. Larena and C. Clarkson,Probing the Cosmological Principle with weak lensing shear,JCAP02(2025) 016 [2411.08560]

2025 arXiv
[38]

Lopes, A

M. Lopes, A. Bernui, C. Franco and F. Avila,Bulk Flow Motion Detection in the Local Universe with Pantheon+Type Ia Supernovae,Astrophys. J.967(2024) 47 [2405.11077]

2024 arXiv
[39]

Rameez,Anisotropy in the cosmic acceleration inferred from supernovae,Phil

M. Rameez,Anisotropy in the cosmic acceleration inferred from supernovae,Phil. Trans. Roy. Soc. Lond. A383(2025) 20240032 [2411.14758]

2025 arXiv
[40]

Célérier,Precision cosmology with exact inhomogeneous solutions of general relativity: The Szekeres models,Phys

M.-N. Célérier,Precision cosmology with exact inhomogeneous solutions of general relativity: The Szekeres models,Phys. Rev. D110(2024) 123526 [2407.04452]

2024 arXiv
[41]

Kalbouneh, C

B. Kalbouneh, C. Marinoni and J. Bel,Multipole expansion of the local expansion rate,Phys. Rev. D 107(2023) 023507 [2210.11333]

2023 arXiv
[42]

Maartens, J

R. Maartens, J. Santiago, C. Clarkson, B. Kalbouneh and C. Marinoni,Covariant cosmography: the observer-dependence of the Hubble parameter,JCAP09(2024) 070 [2312.09875]

2024 arXiv
[44]

Kalbouneh, J

B. Kalbouneh, J. Santiago, C. Marinoni, R. Maartens, C. Clarkson and M. Sarma,Expanding covariant cosmography of the local universe: incorporating the snap and axial symmetry,JCAP02(2025) 076 [2408.04333]

2025 arXiv
[45]

Kristian and R.K

J. Kristian and R.K. Sachs,Observations in cosmology,The Astrophysical Journal143(1966) 379

1966
[46]

MacCallum and G.F.R

M.A.H. MacCallum and G.F.R. Ellis,A class of homogeneous cosmological models,Communications in Mathematical Physics19(1970) 31–64

1970
[47]

Ellis,Relativistic cosmology (republication of 1969 lectures),General Relativity and Gravitation 41(2009) 581–660

G.F.R. Ellis,Relativistic cosmology (republication of 1969 lectures),General Relativity and Gravitation 41(2009) 581–660

1969
[48]

Ellis, D.R

G.F.R. Ellis, D.R. Matravers and R. Treciokas,Anisotropic solutions of the Einstein-Boltzmann equations: I. General formalism,Annals of Physics150(1983) 455. – 34 –

1983
[49]

Ellis, S.D

G.F.R. Ellis, S.D. Nel, R. Maartens, W.R. Stoeger and A.P. Whitman,Ideal observational cosmology., Physics Reports124(1985) 315

1985
[50]

Hasse and V

W. Hasse and V . Perlick,On spacetime models with an isotropic Hubble flow,Class. Quant. Grav.16 (1999) 2559

1999
[51]

Clarkson,On the observational characteristics of inhomogeneous cosmologies, astro-ph/0008089

C.A. Clarkson,On the observational characteristics of inhomogeneous cosmologies, astro-ph/0008089

arXiv
[52]

Clarkson and R

C. Clarkson and R. Maartens,Inhomogeneity and the foundations of concordance cosmology,Classical and Quantum Gravity27(2010) 124008

2010
[53]

Umeh,The influence of structure formation on the evolution of the Universe, PhD thesis, University of Cape Town (2013)

O. Umeh,The influence of structure formation on the evolution of the Universe, PhD thesis, University of Cape Town (2013)

2013
[54]

A. Heinesen,Multipole decomposition of the general luminosity distance hubble law — a new framework for observational cosmology,Journal of Cosmology and Astroparticle Physics2021(2021) 008

2021
[55]

Adamek, C

J. Adamek, C. Clarkson, R. Durrer, A. Heinesen, M. Kunz and H.J. Macpherson,Towards Cosmography of the Local Universe,Open J. Astrophys.7(2024) 001c.118782 [2402.12165]

2024 arXiv
[56]

Tolman,Effect of inhomogeneity on cosmological models,Proceedings of the National Academy of Sciences20(1934) 169 [https://www.pnas.org/doi/pdf/10.1073/pnas.20.3.169]

R.C. Tolman,Effect of inhomogeneity on cosmological models,Proceedings of the National Academy of Sciences20(1934) 169 [https://www.pnas.org/doi/pdf/10.1073/pnas.20.3.169]

1934 doi
[57]

H. Bondi,Spherically Symmetrical Models in General Relativity,Monthly Notices of the Royal Astronomical Society107(1947) 410 [https://academic.oup.com/mnras/article-pdf/107/5-6/410/8072561/mnras107-0410.pdf]

1947
[58]

Kalbouneh, C

B. Kalbouneh, C. Marinoni, R. Maartens, J. Bel, J. Santiago, C. Clarkson et al.,The anisotropic expansion rate of the local universe and its covariant cosmographic interpretation,In preparation (2025)

2025
[59]

Tully, H.M

R.B. Tully, H.M. Courtois and J.G. Sorce,COSMICFLOWS-3,The Astronomical Journal152(2016) 50

2016
[60]

Koksbang,Testing inhomogeneous cosmography in our cosmic neighborhood using cosmicflows-4, Physical Review D111(2025)

S. Koksbang,Testing inhomogeneous cosmography in our cosmic neighborhood using cosmicflows-4, Physical Review D111(2025)

2025
[61]

Codur and C

R. Codur and C. Marinoni,Redshift drift in radially inhomogeneous Lemaître-Tolman-Bondi spacetimes,Phys. Rev. D104(2021) 123531 [2107.04868]. – 35 –

2021 arXiv

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [43]

Kalbouneh, C

B. Kalbouneh, C. Marinoni and R. Maartens,Cosmography of the local Universe by multipole analysis of the expansion rate fluctuation field,JCAP09(2024) 069 [2401.12291]

arXiv 2024

[2] [1]

Di Valentino, O

E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri et al.,In the realm of the Hubble tension—a review of solutions,Class. Quant. Grav.38(2021) 153001 [2103.01183]

arXiv 2021

[3] [2]

Perivolaropoulos and F

L. Perivolaropoulos and F. Skara,Challenges forΛCDM: An update,New Astron. Rev.95(2022) 101659 [2105.05208]

arXiv 2022

[4] [3]

Schöneberg, G

N. Schöneberg, G. Franco Abellán, A. Pérez Sánchez, S.J. Witte, V . Poulin and J. Lesgourgues,The H0 Olympics: A fair ranking of proposed models,Phys. Rept.984(2022) 1 [2107.10291]

arXiv 2022

[5] [4]

E. Abdalla et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,JHEAp34(2022) 49 [2203.06142]

arXiv 2022

[6] [5]

Capozziello, G

S. Capozziello, G. Sarracino and G. De Somma,A Critical Discussion on the H 0 Tension †,Universe10 (2024) 140 [2403.12796]. – 32 –

arXiv 2024

[7] [6]

Bengaly, J.S

C.A.P. Bengaly, J.S. Alcaniz and C. Pigozzo,Testing the isotropy of cosmic acceleration with the Pantheon+and SH0ES datasets: A cosmographic analysis,Phys. Rev. D109(2024) 123533 [2402.17741]

arXiv 2024

[8] [7]

Schwarz and B

D.J. Schwarz and B. Weinhorst,(An)isotropy of the Hubble diagram: Comparing hemispheres,Astron. Astrophys.474(2007) 717 [0706.0165]

arXiv 2007