[Paper Review] The Universe as a Cellular System

Miguel A. Aragón-Calvo|arXiv (Cornell University)|Sep 30, 2014

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper proposes that the cosmic web—comprising voids, walls, filaments, and clusters—functions as a cellular system governed by universal scaling laws (Lewis, Aboav-Weaire, and von Neumann), demonstrating these laws across 30+ orders of magnitude in scale via a cosmological N-body simulation. The key finding is that voids in the large-scale structure of the universe follow the same geometric and topological scaling relations observed in natural cellular systems, suggesting a deep physical universality and offering a potential geometric standard ruler for cosmology.

ABSTRACT

Cellular systems are observed everywhere in nature, from crystal domains in metals, soap froth and cucumber cells to the network of cosmological voids. Surprisingly, despite their disparate scale and origin all cellular systems follow certain scaling laws relating their geometry, topology and dynamics. Using a cosmological N-body simulation we found that the Cosmic Web, the largest known cellular system, follows the same scaling relations seen elsewhere in nature. Our results extend the validity of scaling relations in cellular systems by over 30 orders of magnitude in scale with respect to previous studies. The dynamics of cellular systems can be used to interpret local observations such as the local velocity anomaly as the result of a collapsing void in our cosmic backyard. Moreover, scaling relations depend on the curvature of space, providing an independent measure of geometry.

Motivation & Objective

• To investigate whether the large-scale structure of the universe, particularly the network of cosmic voids, obeys the same scaling laws seen in natural cellular systems such as soap froth and biological tissues.
• To test the validity of three fundamental scaling laws—Lewis, Aboav-Weaire, and von Neumann—across the full dynamic range of void sizes in a cosmological context.
• To explore whether these scaling laws can serve as a geometric standard ruler for cosmology, particularly for measuring the curvature of space.
• To examine the role of gravitational evolution and spatial curvature in shaping the topological and geometric properties of void networks.

Proposed method

• Conducted a high-resolution N-body simulation with 128³ dark matter particles in a 256 h⁻¹ Mpc box, using the ΛCDM cosmology (Ωₘ=0.3, ΩΛ=0.7, h=0.73, σ₈=0.8), evolving from z=80 to z=0.
• Computed a continuous density field using the Lagrangian Sheet method to ensure accurate density estimation, especially in underdense void regions.
• Identified voids via the watershed transform in the Spine pipeline, with a time-continuous void tracking method to link voids across snapshots and minimize over-segmentation.
• Constructed a void-graph dual to the cosmic web, where voids are nodes and shared walls define edges, enabling computation of topological relations (degree, neighbor degrees).
• Tracked individual voids across time to compute the rate of change in void area (dA/dt) as a function of their number of neighbors (n), testing the von Neumann law.
• Applied the Lewis law (n ∝ A), Aboav-Weaire law (mₙ ∝ a + b/n), and von Neumann law (dA/dt ∝ k(n−6)) to quantify scaling behavior at different redshifts.

Experimental results

Research questions

• RQ1 Do cosmic voids in the large-scale structure of the universe obey the same geometric and topological scaling laws (Lewis, Aboav-Weaire, von Neumann) observed in other cellular systems?
• RQ2 How do the scaling relations of voids evolve from high redshift (z=10) to the present (z=0), and what does this imply about the role of gravity in shaping the cosmic web?
• RQ3 Can the observed scaling laws in void networks serve as a geometric standard ruler to independently measure the curvature of space?
• RQ4 What is the critical number of neighbors (n_crit) below which voids collapse, and how does this relate to the von Neumann law and void size evolution?

Key findings

• The Lewis law holds across the entire range of void sizes, with larger voids having a higher average number of neighbors (n ≈ 14 at z=0, consistent with Voronoi predictions of n≈15.54).
• The Aboav-Weaire law is observed at all redshifts, with early-time voids showing a more uniform distribution (higher mₙ for low n), indicating less topological disorder.
• The von Neumann law (dA/dt ∝ k(n−6)) is valid for void evolution, with a critical neighbor count n_crit ≈ 18 at z=0, below which voids collapse on average.
• The simulation shows that voids with radius R < 9 h⁻¹ Mpc collapse, while larger voids expand, consistent with the combined implications of Lewis and von Neumann laws.
• The scaling relations depend on the metric of space, suggesting that deviations from Euclidean geometry (e.g., positive curvature) could be detected through topological constraints on void connectivity.
• The effect of spatial curvature on the von Neumann law is expected to be small (scaling as R⁻²), but the theoretical framework allows for future use of these laws as an independent cosmological standard ruler with high-precision 3D galaxy surveys.