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Observational Challenges for the Standard FLRW Model

Thomas Buchert, Alan A. Coley, Hagen Kleinert, Boudewijn F. Roukema, David L. Wiltshire

arXiv:1512.03313v2astro-ph.COgr-qc

TL;DR

The paper reviews observational challenges to the standard ΛCDM cosmology and relates recent conference results to them. It discusses reported BAO shifts and large-scale structure signals, and concludes that relativistically realistic predictions for structure formation remain underdeveloped.

  • Problem

    The paper addresses the range of observations that significantly disagree with ΛCDM, including CMB large-angle anomalies and structure-formation constraints.

    Source: §1 · pp. 1–2

  • Method

    The paper focuses on individual observational constraints and relates recent reported results to tests of the Friedmann equation and spatial geometry.

    Source: §1 · p. 1, §2.1 · p. 4, §2.2 · p. 4

  • Results

    The SDSS DR7 BAO peak location is reported to be shrunk by 6% across superclusters, unlike the tiny < 0.3% redshift-dependent shift modeled in ΛCDM.

    Source: §4 · p. 10

  • Takeaways & Limitations

    Relativistic cosmological models that account for structure formation need more robust predictions, and the paper argues for developing relativistically realistic observational predictions.

    Source: §5 · p. 12

    The local-boost likelihood is not significantly constrained in directions obscured by the Milky Way because data there are lacking.

    Source: §2.3 · p. 6

Abstract

from arXiv · show

We summarise some of the main observational challenges for the standard Friedmann-Lemaitre-Robertson-Walker cosmological model and describe how results recently presented in the parallel session `Large--scale Structure and Statistics' (DE3) at the `Fourteenth Marcel Grossman Meeting on General Relativity' are related to these challenges.

1. Observational Challenges for the ΛCDM Model

The ΛCDM model has well-known successes but significantly disagrees with a range of observations, whose statistical significance is debated. The section reviews individual observational constraints rather than attempting a full Bayesian comparison of general relativity with ΛCDM plus Newtonian inhomogeneities.

Observational challenges

  • The primordial lithium anomaly is a 5.3σ shortfall of 7Li/H in metal-poor halo stars relative to the ΛCDM CMB expectation, unless new particles such as decaying gravitinos are assumed.Source: §1 · p. 2
  • Planck CMB data reject ΛCDM at p < 0.0024 for conservative data or p < 0.0003 for the best-quality data; hemispherical asymmetry and low-mode alignments also remain about 3σ discrepancies.The large-angle lack of power corresponds to greater observed homogeneity on scales above 10 h−1 Gpc; the text also reports that the anomalies’ significance has increased or remained stable as data precision improved.Source: §1 · p. 2
  • The LRG-void ISW temperature decrement is 9.6 ± 2.2µK, at least 3σ above the ΛCDM expectation of 2.27 ± 0.14µK; Minkowski functionals also show an about 3σ inconsistency.The cited combined measurements across scales yield the 5σ contradiction reported above.Source: §1 · pp. 2–3
  • A combined analysis finds a 5σ contradiction between standard ΛCDM and observations, mainly from differing power in the small- and large-scale parts of the flat-space power spectrum P(k).Weak-lensing constraints also yield an Ωm0 value too low in the σ8–Ωm0 plane at p ≤0.1, unless sterile neutrinos are added.Source: §1 · p. 3
  • Other reported discrepancies include a Lyman α forest BAO signal about 2.5σ from ΛCDM, growth-rate measurements about 2σ below Planck’s expectation, and a multi-survey estimate p ≤0.01 for ΛCDM being correct.Source: §1 · p. 3
  • ΛCDM may also face an overabundance of luminous star-forming galaxies at z ≈10 and difficulty matching Local Group dwarf-galaxy features and halo abundances.Source: §1 · p. 3

2. Observational tests of the FLRW geometry

Model-independent tests matter because standard simulations presuppose FLRW geometry; the section distinguishes tests of Friedmann evolution from tests of spatial geometry below statistical homogeneity.

2.1. Tests of the Friedmann equation

  • The CBL test makes FLRW spatial curvature constant with redshift, while its further-derivative statistic must vanish at every redshift if the Friedmann equations apply.It assumes H and D depend on redshift alone and can discriminate against inhomogeneous models that do not generally obey the late-epoch Friedmann equation.Source: §2.1 · p. 4

2.2. The scale of statistical homogeneity

  • 70–120 h−1 Mpc is the smallest scale where two-point correlations suggest statistical homogeneity, while all N-point correlations place it beyond 700 h−1 Mpc, if reached.Improved survey quality has tended to increase homogeneity-scale estimates; the BAO scale also varies by 6–10% across SDSS DR7 superclusters under a ΛCDM interpretation.Source: §2.2 · p. 5

2.3. Tests of spatial geometry on “small” scales

  • At scales below roughly 100 h−1 Mpc, FLRW spatial geometry is presented as a testable working hypothesis, despite voids around 30 h−1 Mpc and nonlinear density variations on tens of megaparsecs.The authors note that this nonlinear regime is commonly treated with Newtonian N-body simulations, while relativistic simulations have also been pursued.Source: §2.3 · pp. 5–6
  • The kinematic CMB-dipole interpretation requires a Local Group boost of 635 ± 38 km s−1, yet the convergence of bulk flows below about 120 h−1 Mpc remains debated.A claimed simulation-based resolution carries 20% uncertainty, and the authors expect the debate to continue given statistical interpretation complexities.Source: §2.3 · p. 6
  • The spherically averaged Hubble expansion is reported as more uniform in the Local Group rest frame than in the CMB frame, in a model-independent analysis of 4,534 distances.The excerpt does not provide the quantitative size of this difference.Source: §2.3 · p. 6
  • A residual 0.5% distance–redshift anisotropy on scales below about 65 h−1 Mpc is consistent with nonlinear exact Einstein-equation solutions with inhomogeneities no larger than those scales.Source: §2.3 · p. 7
  • The Planck boost direction matches the CMB dipole only at small angular scales; including large-angle multipoles shifts it toward the modulation-dipole anomaly direction.The authors suggest this scale dependence may connect some large-angle CMB anomalies to treating a partly nonkinematic dipole as purely kinematic; an independent NVSS study rejects a purely kinematic radio-galaxy dipole at 99.5% confidence.Source: §2.3 · p. 7

3. Recent developments presented at the MG14 meeting

The MG14 DE3 session covered observational and modelling work on large-scale structure, including statistical, morphological, and general-relativistic topics. The paper focuses mainly on observational cornerstones and challenges to FLRW, while the discussion also raised a statistical question about heavy-tailed distributions.

3. Recent developments presented at the MG14 meeting

  • DE3 covered higher-order and non-Gaussian statistics, morphology, large structures, BAO rulers, mock catalogues, path finders, and abundance statistics, alongside general-relativistic work on backreaction and inhomogeneous cosmologies.The paper focuses mainly on observational issues and current or anticipated challenges to FLRW; modelling work is briefly summarized separately.Source: §3 · p. 7
  • Backreaction and inhomogeneous-cosmology theory were discussed in the separate DE2 session as well as in DE3 talks and a special discussion session.Source: §3 · pp. 7–8
  • The meeting also raised whether heavy-tailed physical-quantity distributions, such as strongly interacting particle orbits [80], may require Levy-distribution analysis, although finite-volume truncation could be more realistic.Source: §3 · p. 8

4. Recent observational results

The DE3 presentations addressed possible systematic errors in ΛCDM analyses and proposed observational tests that could distinguish ΛCDM from relativistic inhomogeneous or non-GR models. Results included a reported environment-dependent BAO shift and a strong Fourier signal, while several projects remain inconclusive or prospective.

Recent observational results

  • Within a few hundred h−1 Mpc, sparse volumes cause high Poisson error, while the practical approach imposes a single theoretical model rather than marginalizing over relativistically valid models.Both approaches introduce a priori assumptions into the analysis.Source: §4 · pp. 8–9
  • 250,000 6dFGS and SDSS galaxy redshifts supported the 150–300 h−1 Mpc Local Hole, and peculiar-velocity maps rejected its being at rest in the CMB frame at 4σ.The authors state that stronger Local Hole evidence or preference for the Szekeres model would imply that systematic errors matter for many, though not all, 1–20 h−1 Gpc analyses.Source: §4 · p. 9
  • Exact Szekeres simulations modeled observational features more closely than FLRW with a kinematic boost or Newtonian N-body simulations, which were rejected at more than 2σ.The simulations incorporated structures below ∼80 h−1 Mpc, matched a Planck-normalized ΛCDM model at larger scales, and included a nonkinematic CMB dipole.Source: §4 · p. 9
  • The ≈105 h−1 Mpc BAO peak was reported shrunk by 6% across SDSS DR7 superclusters, with the shift increasing to 10% as galaxy-pair/supercluster overlap increased.The authors describe this as a qualitative inconsistency with ΛCDM pending quantitative confirmation.Source: §4 · p. 10
  • Mackenzie’s ongoing project will cross-correlate photometric-redshift LRGs with Planck CMB maps to test whether the ∼400 h−1 Mpc supervoid and CMB Cold Spot are physically related.The presentation did not presently reject ΛCDM.Source: §4 · p. 10
  • Majerotto’s CBL-test application found large uncertainties with current data and consistency with FLRW, while Euclid predictions could distinguish Timescape and Tardis curvature relations from ΛCDM [95].The cited models’ average curvature evolves from a small value to strongly negative effective curvature today.Source: §4 · pp. 10–11
  • Voids of ∼10–200 h−1 Mpc are difficult to catalogue because underdensities have high Poisson error, and their cosmological use remains debated.Pisani discussed peculiar velocities and forecasts for Euclid and WFIRST void analyses, assuming FLRW.Source: §4 · p. 11
  • A 4–5σ Fourier signal appeared at 98 ± 3 h−1 Mpc for BCGs and 101 ± 2 h−1 Mpc for Mg II absorption systems [108].The authors suggest possible BAO-scale phase alignment and call for full-scale N-body modeling to test compatibility with a standard power spectrum and random phases.Source: §4 · p. 12

5. Conclusion

The authors do not attempt a Bayesian summary of all evidence, but argue that frequentist tests of individual ΛCDM disagreements are justified pending analyses that include Newtonian–relativistic differences. They call for new, relativistically realistic predictions as observational testing continues.

Conclusion

  • The paper does not attempt a Bayesian summary of all evidence for and against ΛCDM, but argues that frequentist approaches to individual tests are justified pending Bayesian analyses that include Newtonian–relativistic differences.The authors conclude that the disagreements cannot be ignored, regardless of whether they are called rejections, inconsistencies, anomalies, or tensions.Source: §5 · p. 12
  • Predictions for structure-forming general-relativistic cosmologies remain in their infancy, while FLRW predictions will continue to be tested by missions such as Euclid.The authors expect early predictions to become more robust in coming years.Source: §5 · p. 12
  • The authors advocate developing relativistically realistic predictions and suggest that relaxing restrictions such as vanishing spatial curvature across all scales and cosmic history may help new modeling efforts reach consensus.Source: §5 · p. 12
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