An effective description of Laniakea: impact on cosmology and the local determination of the Hubble constant

arXiv:2311.00215 · astro-ph.CO, gr-qc · Submitted 2023-11-01 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: I'm Vera, and with me are Jocelyn and Subrahmanyan, guest researcher.

Jocelyn: Today's paper: "An effective description of Laniakea".

Vera: An effective model describing Laniakea, the gravitational supercluster hosting the Milky Way, impacts cosmological observables and local determinations of the Hubble constant by inducing line-of-sight dependent corrections to luminosity distances.

Jocelyn: First, who's behind it and why it matters.

Title and authors: Vera: So, let's talk about what this paper is actually called and who put it together, because understanding the context helps us figure out how important this research is to us here on the air.

Jocelyn: Yeah, I think starting with the title gives a good idea of the scope; "An effective description of Laniakea: impact on cosmology and the local determination of the Hubble constant" sounds very specific about what they are trying to achieve.

Subrahmanyan: From a theoretical standpoint, I find it interesting that they are focusing on an effective description rather than just simulating everything from scratch, which suggests they are looking for a tractable way to model this complex gravitational influence.

Vera: Exactly, and the authors listed—Giania, Howletta, Saida, and Davisa—are clearly experts in both observational astronomy and mathematical physics working together on this. I'm curious how their specific expertise in peculiar velocity data from Cosmicflows-four helped them define Laniakea as a "gravitational basin of attraction" (<ref:2311.00215#pg0>).

Jocelyn: I wonder if their background in pulsar and sky surveys gave them the right perspective on what kind of peculiar velocity data is most useful for defining these large-scale structures. My work deals with those velocity fields, so I'm keen to know what insights they gained from that specific dataset.

Subrahmanyan: The focus on defining Laniakea using peculiar velocity data from CF4 suggests they are grounding this model in real, measurable motions within the local Universe rather than purely theoretical assumptions about large-scale structure formation (<ref:2311.00215#pg0>).

Vera: It makes sense that they’d want to use CF4 because it’s data that directly maps out these local gravitational basins, and I'm eager to see how those motions translate into the ellipsoid shape they propose (<ref:2311.00215#pg2>).

Jocelyn: So, the title itself suggests this isn't just about a general structure; it’s about how *our* specific location within Laniakea changes our measurements of cosmological constants. That makes it immediately relevant to observational cosmology.

Subrahmanyan: It really highlights the tension between the smooth FLRW model and the highly inhomogeneous environment they are trying to describe, which is exactly where backreaction theory gets complicated (<ref:2311.00215#pg1>).

Vera: And that's what I find so compelling; they’re taking the complexity of being in a supercluster and quantifying its effect on fundamental constants like H zero. It’s data-driven cosmology at its core.

Jocelyn: It definitely sounds like a paper that bridges the gap between large-scale structure observations and precise distance measurements. I'm ready to see how they handle the actual data integration in the next segment.

The paper's summary: Vera: Now that we know who wrote this and what it’re aiming for, let’s talk about what they actually summarized in "An effective description of Laniakea: impact on cosmology and the local determination of the Hubble constant."

Jocelyn: So, essentially, the summary boils down to them creating a model—an ellipsoidal one exhibiting triaxial expansion—to describe Laniakea’s structure using peculiar velocity data from CF4 (<ref:2311.00215#pg0>).

Subrahmanyan: They characterize this structure by defining an ellipsoid with semiaxes of forty-eight point six one, one hundred twenty-eight point seven four, and one hundred sixty-six point three eight Mpc/h, noting that it contracts along the two smaller axes and expands along the longest one by an average rate of about-one point one km/s/Mpc (<ref:2311.00215#pg0>).

Vera: That specific expansion rate is crucial because it’s what drives the corrections they calculate for luminosity distances, moving them away from the standard flat FLRW assumptions (<ref:2311.00215#pg4>).

Jocelyn: They then introduce a line-of-sight dependent function Hlos(theta, phi, z) to approximate the luminosity distance relation as c /

(one +): = Hlos(theta, phi, z) (<ref:2311.00215#pg4>).

Subrahmanyan: This modeling allows them to derive the main contribution to the relative corrections of the luminosity distance being approximately B - / about chi A / chi (<ref:2311.00215#pg4>).

Vera: So, they’re taking the complexity of the geometry and translating it directly into a quantifiable correction term that affects how we measure distances across different redshifts. That's a very direct approach to modeling backreaction effects.

Jocelyn: It’s interesting because they are treating this as a toy model, which is an effective way to gain that qualitative understanding of how anisotropies influence the background geometry in this inhomogeneous environment (<ref:2311.00215#pg2>).

Subrahmanyan: They use this toy model to suggest that overdensities exhibiting triaxial profiles naturally emerge from ellipsoidal gravitational collapse, specifically mentioning a Bianchi I spacetime profile when spatial curvature of the inhomogeneity is negligible during the linear regime (<ref:2311.00215#pg2>).

Vera: It shows how their theoretical framework connects the observed geometry to some established solutions in general relativity, which adds a layer of rigor to their approach.

Jocelyn: So, when you put it all together, they’re using velocity data to define a specific three dee shape for Laniakea and then mathematically linking that shape’s expansion dynamics to distance measurements across various redshifts (<ref:2311.00215#pg4>).

Subrahmanyan: That's the core summary: modeling Laniakea as an expanding ellipsoid to derive line-of-sight dependent corrections that impact cosmological observables (<ref:2311.00215#pg7>).

The paper's improvements: Vera: Moving on to what they improved, the authors explicitly show how their ellipsoidal model improves upon the traditional working assumption of spherical symmetry, and they quantify that improvement statistically.

Jocelyn: It’s not just that it’s a different shape; it’s that this ellipsoidal model is preferred over the spherical one with a large Bayesian Information Criterion difference of BIC about-two hundred eighty-three (<ref:2311.00215#pg7>).

Subrahmanyan: That BIC value suggests that the complexity added by accounting for triaxial expansion is statistically justified, implying the spherical model is too simplistic for describing Laniakea's actual influence (<ref:2311.00215#pg7>).

Vera: And they show that this modeling leads to measurable shifts in H zero with H SN Ia zero about zero point five km/s/Mpc and H SBF zero about one point one km/s/Mpc (<ref:2311.00215#pg5>).

Jocelyn: So, the improvement isn't just theoretical; it has direct, measurable consequences for the Hubble constant derived from actual observational data sets like SN Ia and SBF. That’s a strong demonstration of how this modeling works in practice.

Subrahmanyan: The paper also highlights that they are using peculiar velocity data from Cosmicflows-four to define Laniakea as a "gravitational basin of attraction hosting the Milky Way," which is an important methodological improvement (<ref:2311.00215#pg0>).

Vera: It’s a significant methodological step because it grounds the geometry in actual motions observed in the Universe, making the model more physically grounded than just picking arbitrary parameters for a sphere.

Jocelyn: And I think that's what makes it so useful for pulsar and sky surveys too; if we can use velocity data to define these basins, maybe we can look for similar anisotropies in the kinematics of things we observe across different scales.

Subrahmanyan: The paper also suggests that the interior of this ellipsoid is assumed to be "spatially flat" and homogeneous at rest in its comoving frame, which simplifies the internal dynamics while still allowing for the external anisotropy (<ref:2311.00215#pg2>).

Vera: It’s a clever simplification; it keeps the focus on how the large-scale environment affects us without getting bogged down in every tiny detail of internal turbulence, which makes it more applicable to cosmological inference.

Jocelyn: So, these improvements mean we have a way to test if our current distance measurements are systematically skewed by this local gravitational influence, providing a new tool for cross-validation.

Conclusion: Vera: We’ve gone through the whole paper, and it seems like the main conclusion is that while Laniakea's backreaction is well-modeled by their ellipsoidal model, it doesn't quite solve the current cosmological tensions we see.

Jocelyn: That’s what they concluded: Laniakea’s gravitational backreaction likely worsens the current Hubble tension rather than resolving it (<ref:2311.00215#pg7>). It seems like a prediction that's consistent with what we currently observe across different probes.

Subrahmanyan: From a theoretical viewpoint, they emphasize that this study is important because it underscores the necessity of understanding local environments for future mapping and modeling of the Universe (<ref:2311.00215#pg7>).

Vera: So, in summary, we have an effective description of Laniakea as a triaxial ellipsoid using real velocity data, which predicts specific shifts in H zero depending on whether you look at SN Ia or SBF data. It’s a valuable tool for local constraints.

Jocelyn: I think what this means for us is that we should keep looking for these kinds of systematic effects when we analyze our own pulsar timing and large-scale structure observations, because the paper shows they are real and quantifiable.

Subrahmanyan: That's right, the work on "An effective description of Laniakea: impact on cosmology and the local determination of the Hubble constant" provides a very useful framework for incorporating these complex gravitational interactions into cosmological inference (<ref:2311.00215#pg7>).

Vera: It’s a good reminder that even when we look at our closest neighbors, there are systematic effects to account for if we want the most precise cosmology possible. That’s all for this session on this paper.

Leonardo Giani, Cullan Howlett, Khaled Said, Tamara Davis, Sunny Vagnozzi

School of Mathematics and Physics, The University of Queensland · Department of Physics, University of Trento · Trento Institute for Fundamental Physics and Applications · Istituto Nazionale di Fisica Nucleare

astro-ph.CO, gr-qc

Submitted: 2023-11-01

Updated: 2026-10-05

Comments: Updated to match the corrections from the Erratum. Eighteen pages + references, 13 figures, 1 appendix, title and abstract slightly changed. Comments are welcome!

Journal ref: JCAP 2401 (2024) 071

DOI: 10.1088/1475-7516/2024/01/071

Code: https://github.com/Leolardo/Laniakea

Project page: https://leolardo.github.io/Laniakea

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 80/100

The gist: Modeling the Laniakea supercluster as a triaxially expanding ellipsoid and correcting low-redshift distance measurements for its gravitational backreaction shifts the inferred Hubble constant upward

Key concepts

Laniakea Model: This is an effective model describing Laniakea not as a sphere, but as an ellipsoid with three different expansion rates along its axes. It is constructed using peculiar velocity data to define it as a gravitational basin that hosts the Milky Way, capturing its spatial anisotropy.
Luminosity Distance Corrections: Because Laniakea is inhomogeneous, the standard cosmological distance formulas are modified. The model introduces a line-of-sight dependent function to approximate how observed redshift relates to cosmological redshift, leading to corrections in luminosity distance calculations.
Hubble Tension: This refers to the discrepancy between different measurements of the Hubble constant (the rate of expansion of the universe) obtained from early-universe probes and late-universe probes. The paper finds that Laniakea's corrections shift inferred $H_0$ values, which is consistent with worsening this tension.
Triaxial Expansion: This describes the shape of Laniakea as an ellipsoid that is not uniform in all directions. It has three distinct semiaxes (lengths) and different expansion rates along these axes, meaning its structure is stretched differently in various spatial directions.

Terminology

Hubble Tension — 8× in this paper · explained in 9 episodes
Bulk Flow — 6× in this paper
Homogeneity — 6× in this paper · explained in 2 episodes
Laniakea Comoving Frame — 4× in this paper
Surface Brightness Fluctuations — 4× in this paper
Accuracy — 2× in this paper · explained in 1 episode
Dark Energy — 2× in this paper
Anisotropy — 1× in this paper · explained in 3 episodes
Bayesian Information Criterion — 1× in this paper
Consistency — 1× in this paper · explained in 3 episodes
Cooperation — 1× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Cosmological Principle — 1× in this paper
Hamiltonian Monte-Carlo — 1× in this paper
Markov Chain Monte Carlo — 1× in this paper
Trento Institute for Fundamental Physics and Applications — 1× in this paper
Velocity Dispersion — 1× in this paper · explained in 2 episodes

Summary

Modeling the Laniakea supercluster as a triaxially expanding ellipsoid and correcting low-redshift distance measurements for its gravitational backreaction shifts the inferred Hubble constant upward by roughly 0.5–1.1 km/s/Mpc, seemingly worsening the Hubble tension rather than alleviating it.

The model

The authors derive an effective description of Laniakea, the gravitational supercluster hosting the Milky Way, using peculiar velocity data from Cosmicflows-4 (CF4). They fit an ellipsoid to the 4079 cells defining the structure, obtaining semiaxes of 48.61, 128.74, and 166.38 Mpc/h, centered at supergalactic coordinates SGX = −9.23, SGY = −47.06, SGZ = 85.08. The interior is treated as homogeneous and spatially flat, with three different scale factors (a Bianchi I line element), while the exterior is standard flat FLRW. The authors assume small anisotropies, Hi = H̄ + ∆Hi with ∆Hi/H̄ ≪ 1, and neglect the redshift evolution of the anisotropies given Laniakea's low redshift. They subtract the bulk flow (vBF components −164 ± 4, 19 ± 2, −96 ± 3 km/s) to work in the Laniakea Comoving Frame.

Fitting the expansion rates

An MCMC fit maximizes a Gaussian likelihood comparing predicted radial velocities to reconstructed ones, with flat priors −6 < ∆Hi < 6 km/s/Mpc. Three dispersion treatments are tested:

Linear dispersion only: χ2ν = 7.903, p < 10−5 (poor fit)
Non-linear only (σnl = 170 km/s): χ2ν = 0.987, p = 0.72 (adopted)
Combined in quadrature: χ2ν = 0.751, p = 1

The adopted best fit gives ∆Ha = −3.40 ± 0.28, ∆Hb = −0.65 ± 0.13, ∆Hc = 0.69 ± 0.03 km/s/Mpc: the ellipsoid contracts along the two smaller axes and expands along the longest one, with an average expansion of ∼ −1.1 km/s/Mpc. A spherical model instead yields ∆Hsph = 0.39 ± 0.02, and ∆BIC ≈ −283 favors the triaxial model. Residuals are Gaussian but spatially non-random, suggesting internal structures not captured by the homogeneous profile.

Distance corrections

Different expansion rates inside versus outside induce line-of-sight-dependent corrections to comoving distances, δdB/d̄B ≈ ∆χA/χ̄B. The authors identify two concurring effects: a quadrupolar pattern from the triaxial expansion, and a hemispherical asymmetry from the observer's offset from the ellipsoid's center. Corrections are of order ∼ 2 − 3% and are approximately constant within the ellipsoid, vanishing asymptotically outside.

Impact on H0

Applying corrections to two low-redshift datasets:

Pantheon+ SN Ia: corrections up to 1.8% for the low-z subset; shift ∆H0 ≈ 0.5 km/s/Mpc
63 SBF measurements from the MASSIVE survey: larger average corrections (sources are closer); shift ∆H0 ≈ 1.1 km/s/Mpc

The authors note the SH0ES collaboration also finds a larger H0 (≈ 0.3 km/s/Mpc) when restricting to 0.06 > z > 0.015, corroborating our results. They find Laniakea's average density contrast (⟨δ⟩ = 0.012) is consistent with ΛCDM, and a surrounding sphere of radius ≈ 110 Mpc gives δ ∼ −0.06, disfavoring a local-void resolution of the tension. They caution that voids in the annular region 110–400 Mpc outside Laniakea could still balance and overcome the backreaction from Laniakea, motivating future work.

Improvements for AI systems

Line-of-sight-dependent distance correction module. Add a pluggable correction layer that computes δd B/d̄ B ≈ Δχ A/χ̄ B from a directional Hubble field H los(θ, ϕ, z) inside a bounded region, so any distance-based inference pipeline can be re-run with and without the correction to quantify systematic bias.
Ellipsoid-fitting geometry estimator. Implement a robust best-fit triaxial ellipsoid (center, semiaxes, rotation angles) over point clouds of cells/galaxies, with goodness-of-fit via conformal rescaling to a unit sphere (the paper reports mean radius 0.97, std 0.23), enabling automatic detection of anisotropic local structures.
Triaxial expansion-rate MCMC fitter. Provide a likelihood log L = −½ Σ n (v th r̃ − v rcst r̃)2/σ n2 with flat priors on ΔH i and cell-averaging over grid vertices, returning posterior constraints on ΔH a, ΔH b, ΔH c and χ2 ν, so AI systems can infer anisotropic expansion from peculiar-velocity maps.
Model-selection comparator (BIC + residual diagnostics). Automatically compare triaxial vs spherical models via ΔBIC (paper finds ΔBIC ≈ −283 favoring triaxial) and flag non-random residual spatial structure, preventing premature adoption of isotropic approximations.
Dispersion-model sensitivity sweep. Systematically evaluate fits under σ lin, σ nl, and quadrature combinations, reporting parameter stability and p-values, so AI systems report uncertainty ranges rather than single-point estimates when noise modeling is ambiguous.
Redshift-identification disambiguation. Enforce explicit choice between same observed redshift (ε = 0) and same emission time treatments, since the paper shows η ≠ 0 enters only at second order and the two conventions coincide when z = z̄—preventing silent double-counting of peculiar-velocity corrections.
Peculiar-velocity double-counting guard. Detect when a catalog's covariance matrix already includes PV corrections and strip those for objects inside the modeled region before applying backreaction corrections, as the paper warns consistency would then require to recompute the full Pantheon+ covariance matrix.
Low-z cosmographic H0 estimator with directional corrections. Fit μ i = 5 log[(cz i/H 0)(1 + ½(1−q 0)z i)(1 + Δχ i/χ i)] + 25 using diagonal errors, yielding shifts like ΔH 0 ≈ 0.5 (SN Ia) and ≈ 1.1 km/s/Mpc (SBF), so AI systems can quantify environment-induced bias on H 0.
Sky-map correction visualizer. Generate full-sky maps of relative distance corrections for isotropic source distributions up to z = 0.1, separating quadrupolar (triaxial) and hemispherical (observer-offset) contributions, aiding interpretation of anisotropic residuals in low-z datasets.
Backreaction sign/void-balance reasoner. Encode the finding that an overdense region with slower internal expansion shifts inferred H 0 upward, and support testing whether surrounding voids in the 110–400 Mpc annulus could balance and overcome the backreaction from Laniakea, enabling hypothesis ranking for Hubble-tension scenarios.