Warped Cosmos: The Secret Life of the Local Universe ✦

Original: "Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood"

· Marco Galoppo, Thomas Buchert, Pierre Mourier

arXiv:2605.05454v1 · 2026-05-06 · CC BY 4.0 · ⏱ 3 min · Cosmology General Relativity

For the first time, the averaged spatial curvature around the Milky Way has been measured, reaching 10% of the energy budget and not converging to the standard cosmological model.

Abstract

For the first time, a direct calculation of spatially averaged dynamical quantities in the local Universe has been carried out using the Cosmicflows-4++ reconstruction and the covariant scalar averaging formalism. Averaged over regions around the Galaxy, density, expansion rate, spatial curvature, and kinematic backreaction have been extracted for comoving radii up to 300 Mpc/h. The resulting scale-dependent energy budget reveals a nontrivial structure, including a large-scale void shell surrounding the local cosmic web. On all scales studied, a significant contribution of average spatial curvature on the order of 10% is found. Kinematic backreaction remains negligible, reaching at most 1% at the smallest radii (30 Mpc/h). Convergence to the global ΛCDM background is not observed on these scales.

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Context

Modern cosmology rests on the idea that the expansion of the Universe is homogeneous and isotropic on large scales. However, the local distribution of matter, resembling a cosmic web of galaxies and clusters, can disrupt this idyll. Georges Lemaître and Edwin Hubble laid the foundations, but only now, with detailed velocity field reconstructions, can we measure how inhomogeneities affect local dynamics through gravity and spacetime curvature. Whether small-scale ripples accumulate into global effects is known as the backreaction problem, and the answer could change our understanding of dark energy.

Methods

The researchers used the latest Cosmicflows-4++ reconstruction—a three-dimensional map of the local Universe built from redshift data and peculiar velocities of thousands of galaxies using numerical simulations. By applying a covariant averaging scheme for scalars in general relativity (Buchert's formalism), they computed the average density, expansion rate, and scalar spatial curvature within spherical domains. A key insight was the algebraic correspondence between the Newtonian and Einsteinian pictures, which allowed interpreting the effective 'Newtonian curvature,' calculated from density and flow kinematics, as genuine curvature in general relativity.

Results

It turned out that the contribution of the averaged spatial curvature ΩR consistently stays around 10% on all scales studied—from 30 to 300 Mpc/h. Moreover, the sign of the curvature changes: in the immediate vicinity (up to ~50 Mpc/h) space has negative curvature, corresponding to a local void; then (50–200 Mpc/h) it becomes positive, outlining a giant shell of superclusters; and again negative at larger distances, pointing to a vast emptiness surrounding the local cosmic web. In contrast, the kinematic backreaction ΩQ does not exceed 1% even at the smallest radii. Remarkably, the total energy budget within a 300 Mpc/h volume never approached the global ΛCDM model values: matter density ΩM and the ΩΛ parameter fluctuate noticeably, and the cosmic microwave background only sets distant boundary conditions.

Implications

These findings mean that the local Universe is still far from statistical homogeneity, and using global cosmological parameters derived from the cosmic microwave background could systematically bias data analysis in the nearby cosmos. The averaged curvature acts as the main carrier of information about the backreaction history accumulated over billions of years, and its contribution to dynamics does not vanish with increasing scale. Consequently, precise cosmographic tests, including standard candles, must account for regional variations in curvature and expansion.

Future development

In the future, with new peculiar velocity surveys (DESI, 4MOST) and the development of relativistic Lagrangian reconstruction methods, we will be able to map the scale dependence of ΩR more accurately and possibly go beyond linear approximations. This will not only refine the boundaries of local inhomogeneity but also test alternative cosmological scenarios where dark energy is partially or fully replaced by backreaction effects.

Impact

The results will impact observational cosmology (standard candles, baryon acoustic oscillations), the interpretation of low-multipole CMB data, and numerical simulations of large-scale structure.

Next steps

Immediate next steps include applying nonlinear reconstructions in the Lagrangian formulation and analyzing data from new spectroscopic surveys to test the robustness of the observed pattern.

Key open problems

This work directly ties into the unsolved problem of dark energy: if backreaction and curvature can explain the accelerated expansion on local scales, it would reduce the need for a cosmological constant. It also raises the question of the correct averaging procedure in general relativity.

🎯 It's like a cosmic nesting doll: we live in a local bubble nested within a supercluster, which in turn is embedded in an even larger void stretching hundreds of megaparsecs.

\Omega_M^{\mathcal{D}} + \Omega_\Lambda^{\mathcal{D}} + \Omega_R^{\mathcal{D}} + \Omega_Q^{\mathcal{D}} = 1

The sum of contributions from matter (including dark matter), dark energy (lambda term), average spatial curvature, and kinematic backreaction equals one in any compact region.

Q_{\mathcal{D}} = \frac{2}{3}\langle (\Theta - \langle\Theta\rangle)^2 \rangle - 2\langle \sigma^2 \rangle

Defined by the variance of local expansion and the averaged square of the shear tensor; it quantifies how inhomogeneities alter the average expansion.

\mathcal{R} = 2\Lambda + 16\pi G \varrho + \Theta^i_j \Theta^j_i - \Theta^2

Within the Newton–GR correspondence, it allows computing spatial curvature, physically interpreted as a deviation from Euclidicity, using density and velocity gradients.

Key numbers

contribution of average curvature Ω_R: ≈ 10% on all scales (30–300 Mpc/h)
maximum contribution of kinematic backreaction Ω_Q: ≈ 1% at 30 Mpc/h
radius of outer void: > 200 Mpc/h
reconstruction resolution: ≈ 8 Mpc/h
data redshift: z ~ 0.1 (approximately 300 Mpc/h)

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