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arxiv: 1907.08684 · v1 · pith:IAC6E5YEnew · submitted 2019-07-19 · 🌌 astro-ph.CO · gr-qc

CMB dipoles and other low-order multipoles in the quasispherical Szekeres model

Robert G. Buckley , Eric M. Schlegel This is my paper

Pith reviewed 2026-05-24 18:51 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords Szekeres modelCMB dipolequadrupoleoctupoleinhomogeneous cosmologyLTB modelquasisphericalmultipoles
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The pith

Quasispherical Szekeres models permit a significant CMB quadrupole consistent with the observed dipole, unlike LTB voids that force the observer near the center.

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

The paper tests whether quasispherical Szekeres models, which drop spherical symmetry, can accommodate the observed CMB dipole with an observer in a less special location than the center of an LTB void. It shows that the allowed observer region remains small yet is not geometrically privileged in the same way. The key result is that certain parameter choices produce a sizable quadrupole while still matching the dipole, offering a possible route to the observed quadrupole and octupole anomalies. This matters for assessing whether large-scale inhomogeneity can explain CMB features without strong Copernican violation.

Core claim

In the quasispherical Szekeres model the observer is still restricted to a limited spatial region to reproduce the measured dipole, but that region lacks the exact centering demanded by LTB voids. Unlike LTB cases, where quadrupole and octupole amplitudes must stay small near the center, selected Szekeres configurations allow a substantial quadrupole while remaining dipole-consistent.

What carries the argument

The quasispherical Szekeres metric, a non-spherically-symmetric generalization of the LTB dust solution, used to integrate null geodesics and compute low-order CMB multipoles for off-center observers.

If this is right

  • The observer location in viable Szekeres models is constrained but does not coincide with a symmetry center.
  • A large quadrupole can coexist with the observed dipole amplitude.
  • Szekeres models supply a candidate mechanism for the reported quadrupole and octupole anomalies.
  • Consistency with the dipole does not require exact spherical symmetry around the observer.

Where Pith is reading between the lines

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

  • If the dipole-matching region proves compatible with supernova data, it would weaken the Copernican objection to Gpc-scale voids.
  • Higher-order multipoles or polarization patterns could distinguish Szekeres from LTB explanations.
  • The same metric could be checked against BAO or weak-lensing surveys to test whether the required inhomogeneity scale conflicts with other large-scale observations.

Load-bearing premise

Szekeres models can be tuned to reproduce the dipole without violating supernova distances or large-scale homogeneity constraints.

What would settle it

A calculation or observation showing that every Szekeres parameterization matching the dipole forces the quadrupole to remain as small as in LTB models would disprove the claim.

Figures

Figures reproduced from arXiv: 1907.08684 by Eric M. Schlegel, Robert G. Buckley.

Figure 2
Figure 2. Figure 2: FIG. 2. The six geodesics used to calculate the dipole at a par [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Density plots of (a) model 1, (b) model 2, and (c) model [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Magnitudes and directions of dipoles in a two [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a): magnitudes of the Szekeres dipoles at various [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The total dipole magnitudes across models 1 (a), 2 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The primary quadrupole coefficient [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The full cmb sky induced by the Szekeres void of model [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) The quadrupoles at all tested points in model 2, [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

Several authors have previously shown that Gpc-scale void based on the spherically symmetric LTB model can provide a good fit to certain cosmological data, including the SNIa data, but it is only consistent with the observed CMB dipole if we are located very close to the center, in violation of the Copernican principle. In this work we investigate the more general quasispherical Szekeres model, which does not include spherical symmetry, in order to determine whether this option may be less constricting. We find that the observer is still constrained to a small region, but it is not as geometrically ``special'' as the center of an LTB void. Furthermore, whereas the quadrupole and octupole near the center of an LTB void are necessarily small, certain Szekeres models can include a significant quadrupole while still being consistent with the observed dipole, hinting that Szekeres models may be able give an explanation for the observed quadrupole/octupole anomalies.

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

1 major / 2 minor

Summary. The paper examines whether quasispherical Szekeres models, which lack spherical symmetry, can accommodate an observer location that reproduces the observed CMB dipole without requiring the observer to be at a geometrically special center (as in LTB voids). It further claims that certain parameter choices allow a non-negligible quadrupole while remaining consistent with the dipole, suggesting these models might explain observed low-multipole CMB anomalies.

Significance. If the constructed models can be shown to remain viable when confronted with the full set of cosmological constraints invoked in the introduction (SNIa distances and large-scale homogeneity), the result would indicate that Szekeres geometries offer more flexibility than LTB for fitting CMB multipoles without extreme Copernican violation. The work supplies concrete examples of the dipole-quadrupole trade-off, which is a useful technical step even if broader consistency checks are still required.

major comments (1)
  1. [Results / Discussion (around the quadrupole examples)] The central claim that the models remain 'consistent with the observed dipole' while permitting a significant quadrupole rests on matching only the dipole via observer location and metric functions. However, the introduction invokes SNIa data and large-scale homogeneity as key constraints that LTB models must satisfy; the manuscript does not recompute the luminosity-distance relation along the observer's past light cone or impose near-homogeneity on scales ≳100 Mpc for the chosen Szekeres examples. This check is load-bearing for the claim that the models 'may be able to give an explanation for the observed quadrupole/octupole anomalies.'
minor comments (2)
  1. [Methods] Notation for the free functions in the Szekeres metric and the precise definition of the observer's past light cone integration should be stated explicitly in the methods section to allow reproduction of the dipole and quadrupole calculations.
  2. [Abstract] The abstract states findings on observer location and quadrupole behavior but supplies no equations, numerical methods, data comparisons, or error analysis; adding a brief summary of the integration procedure and the specific parameter values used for the 'certain Szekeres models' would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed report and the opportunity to clarify the scope of our work. We address the single major comment below.

read point-by-point responses

  1. Referee: [Results / Discussion (around the quadrupole examples)] The central claim that the models remain 'consistent with the observed dipole' while permitting a significant quadrupole rests on matching only the dipole via observer location and metric functions. However, the introduction invokes SNIa data and large-scale homogeneity as key constraints that LTB models must satisfy; the manuscript does not recompute the luminosity-distance relation along the observer's past light cone or impose near-homogeneity on scales ≳100 Mpc for the chosen Szekeres examples. This check is load-bearing for the claim that the models 'may be able to give an explanation for the observed quadrupole/octupole anomalies.'

    Authors: We agree that the specific Szekeres examples used to illustrate a non-negligible quadrupole were not subjected to the full set of constraints (SNIa luminosity distances and near-homogeneity on ≳100 Mpc scales) that are referenced in the introduction for context with prior LTB studies. Our manuscript is narrowly focused on the geometric question of whether quasispherical Szekeres models permit an observer region that matches the observed CMB dipole while allowing a larger quadrupole than is possible near the center of an LTB void. The abstract and discussion carefully qualify the result as a 'hint' that such models 'may be able' to address the anomalies, rather than claiming a complete cosmological solution. Because the luminosity-distance and homogeneity calculations are computationally demanding and lie outside the primary technical scope (dipole-quadrupole trade-off), they were not performed. We will add a short clarifying paragraph in the discussion section stating that these additional consistency checks are required before the models can be considered viable and that they are left for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via model parameterization.

full rationale

The abstract and described claims rest on exploring quasispherical Szekeres metrics to parameterize observer location for dipole matching while permitting quadrupole. No equations, fitting procedures, or self-citations are shown that reduce predictions to inputs by construction. The work contrasts with LTB models without invoking load-bearing self-citations or ansatzes. This is the common case of an honest non-finding; the central claim has independent content from explicit model construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claims rest on unstated modeling assumptions about the Szekeres metric and its ability to reproduce observed multipoles.

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Reference graph

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