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A Bayesian catalog of 100

high-significance voids in the Local Universe

Rosa Malandrino

Institut d’Astrophysique de Paris

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In collaboration with:

Guilhem Lavaux (IAP), Benjamin Wandelt (Johns Hopkins), Stuart McAlpine (Stockholm University) and Jens Jasche (Stockholm University)

Les Houches - Dark Universe

15/07/2025

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Background

Context

Large-scale structure of the Universe

Focus on cosmic voids, i.e. underdense regions of space

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Underdensities of the primordial field evolved under the effect of cosmic expansion and gravity

Credits: Millennium Simulation

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Les Houches - Dark Universe

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Why voids?

  • dominated by dark energy, study cosmic acceleration
  • gravitational effect of neutrinos is not negligible
  • the features of the initial conditions aren’t washed out by gravitational collapse

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Astrophysics:

  • density environment affects properties of objects like galaxies

Less dark matter:

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Les Houches - Dark Universe

Voids are time capsules that preserve information from the early Universe

Credits: NASA SVS

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Void detection: a challenging task

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Gregory and Thompson (1978)

Look for empty regions in galaxy maps

DESI collaboration (2025)

Intrinsic issues:

  • galaxies are biased tracers
  • survey mask: how do you “fill the gaps”?
  • magnitude limits: risk of detecting false positives

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Is it just an observational problem?

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Rosa Malandrino

Les Houches - Dark Universe

We propose a statistical method to detect high-significance voids and determine their properties in a Bayesian framework

What if we knew the exact positions of all galaxies?

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Intrinsic issues:

  • one realization of the Universe
  • no unique void definition
  • not well defined centers and boundaries

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Colberg (2008)

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BORG: a large scale probabilistic inference engine

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generate ICs

forward simulate

  • fully differentiable cosmology simulation

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predict observables

impaint tracers

  • galaxy bias
  • redshift distortions
  • light-cone effects

constrain by data

  • likelihood comparison

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Hamiltonian Monte Carlo

Slide credit:

J.Jasche & G. Lavaux

Jasche & Wandelt (2014)

Jasche, Leclercq, Wandelt (2015)

Lavaux & Jasche (2016)

Jasche & Lavaux (2019)

Lavaux, Jasche, Leclercq (2019)

Bayesian

Origin

Reconstruction from

Galaxies

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Constrained simulations of the large-scale structure

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Galaxy positions

Manticore Local, McAlpine et al. (2025)

2M++ galaxy compilation

Set of possible initial conditions

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Posterior realizations of the present day large-scale structure

Lavaux & Hudson (2011)

BORG

N-body

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Voids in constrained simulations

Overlap the centers from different realizations on the same space

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Run the VIDE void finder on individual realizations

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Les Houches - Dark Universe

VIDE, The Void IDentification and Examination toolkit, Sutter et al. (2014), https://code.cosmicvoids.net/

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Voids in constrained simulations

  • Classical detection problem
  • How many points make a cluster significant?
  • What’s the probability of having clusters of n points by chance?
  • P(n - 1) is a Poisson distribution, 5𝜎 detection threshold (~ 6×10-7)

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Les Houches - Dark Universe

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Voids in the Local Universe: probability distributions

Combining contributions from different realizations catalog of 100 voids with posterior distributions of their properties

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Les Houches - Dark Universe

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Catalog of voids in the Local Universe

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Les Houches - Dark Universe

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The actual shape of voids

  • Voronoi tessellation on the tracers of the density field, e.g. galaxies or halos
  • merging underdense cells with a watershed transform (Platen et al., 2007)
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  • irregular object summarizable with center and effective radius

Sutter et al. (2014)

  • Voronoi tessellation on the tracers of the density field, e.g. galaxies or halos
  • merging underdense cells with a watershed transform (Platen et al., 2007)
  • irregular object summarizable with center and effective radius
  • Voronoi tessellation on the tracers of the density field, e.g. galaxies or halos
  • merging underdense cells with a watershed transform (Platen et al., 2007)
  • irregular object summarizable with center and effective radius

Credits: Francesco Bellelli

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Rosa Malandrino

Les Houches - Dark Universe

VIDE, The Void IDentification and Examination toolkit, Sutter et al. (2014), https://code.cosmicvoids.net/

altitude = density

filaments

clusters

voids

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Shape of voids: Voronoi clouds

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Les Houches - Dark Universe

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Shape of voids: truncated Voronoi clouds

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Les Houches - Dark Universe

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Voronoi cloud vs average density field

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Rosa Malandrino

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Full shape of the catalog

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https://voids.cosmictwin.org

interactive version of this plot

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How can we use the catalog?

  • CMB cross-correlation:
    • cosmic shear density maps
    • Sunyaev-Zel’dovich maps
    • Integrated Sachs-Wolfe effect
  • void summary statistics
  • gravitational lensing
  • void summary statistics

Template for density environment, learn a bunch of astrophysics!

Cosmology?

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Les Houches - Dark Universe

Credit: ESA, Planck

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Take home messages

  • catalog of high-significance voids, likely to be “real” voids
  • Bayesian characterization of statistical uncertainties
  • well defined centers and boundaries
  • template for density environments (e.g. galaxy evolution)
  • cosmology: gravitational lensing and CMB cross correlations
  • ongoing: bigger simulated volume constrained by SDSS up to z<0.7

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https://voids.cosmictwin.org

arXiv:2507.06866

To stare into the void(s)

Rosa Malandrino

Thank you for your attention!

Les Houches - Dark Universe

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Backup

Credit: Chris Wren and Kenn Brown/mondoworks

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Clustering strategy

Agglomerative clustering:

  • every point is a cluster of n = 1
  • merge clusters separated by the shortest distance
  • increase the linking distance at every iteration
  • stop at a determined threshold

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Radius bins to compare similarly-sized voids

Maximum distance between clusters: mean void radius in the bin

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Les Houches - Dark Universe

Image credits: IBM

distance

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Agglomerative clustering

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Credits: https://primo.ai/index.php/Hierarchical_Clustering;_Agglomerative_%28HAC%29_%26_Divisive_%28HDC%29

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Unconstrained voids: Poisson distribution

What’s the probability of having clusters of n points by chance?

5𝜎 detection threshold (~ 6×10-7)

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Les Houches - Dark Universe

n = 13

n = 16

n = 9

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Probability distributions estimation

Choice of binning is arbitrary and might separate points belonging to the same cluster continuous binning strategy

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Les Houches - Dark Universe

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Probability distributions estimation

Each point can be counted multiple times probability distribution obtained with a weighted kernel density estimation (KDE)

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Les Houches - Dark Universe