H.M. Courtois1, A. Dupuy2, D. Guinet1, G. Baulieu1, and F. Ruppin1 1 Université Claude Bernard Lyon 1, IUF, IP2I Lyon, 69622 Villeurbanne, France 2 Korea Institute for Advanced Study, 85, Hoegi-ro, Dongdaemun-gu, Seoul 02455, Republic of Korea

Received A&A Oct 31, 2022- AA/2022/45331; Accepted date arXiv:2211.16390v1 [astro-ph.CO] 29 Nov 2022

**Intro to the article By Dr Beck**

This is the first in a small series of articles reporting density variations in the gravitational or spacetime fields amongst the large structures identified previously by the Dame Prof Dr Hélène Courtois team, using the CosmicFlows-4 program. It ushers in a new way to search for what has been called “dark matter/dark energy”, although it’s character is undefined at present. Singularities and discontinuities in spacetime will also be exposed by this technique. Here, Dame Hélène Courtois explains a simple walk in the Universe in the mode of the supercluster Laniakea – her discovery – her revolution in thinking.

Le conformisme, Hélène Courtois n’a jamais été très amie avec lui. Petite déjà, avide de comprendre le monde qui l’entourait, elle refusait d’appliquer, sans autre questionnement, ce qu’on lui imposait.* “J’étais contre et je le suis toujours. Je n’apprends pas quelque chose que je ne comprends pas, que je ne maîtrise pas. Qui plus est, je ne supporte pas l’autorité. C’est pour cette raison que je me suis faite renvoyer de la maternelle”*, raconte-t-elle, aujourd’hui, avec malice.

She is a Knight Officer of the French Republic, Legion d’Honour; a Knight of Academics with Palm Leaves; a Doctor d’Etat; a Professor at Lyons. She is beyond being a role model.

*ABSTRACT*

“This article publicly releases three-dimensional reconstructions of the local Universe gravitational field below z=0.8 that were computed using the full catalogue CosmicFlows-4 of 56,000 galaxy distances and its sub-sample of 1,008 type Ia supernovae distances. The article also provides some first CF4 measurements of the growth rate of structure using the pairwise correlation of peculiar velocities fσ8 = 0.44(±0.01) and of the bulk flow in the Local Universe of 200 ± 88 kms1 at distance 300 h−1.

Key words. Cosmology: large-scale structure of Universe

**1. Introduction **

“Peculiar (i.e gravitational) velocities of galaxies are a robust probe for the search for dark matter on large scales in the Universe. Their radial component can be computed in a basic way directly from galaxy distances. This method is immensely prone to a variety of Malmquist biases. In order to map the local dark matter distribution and to measure various cosmological parameters, the modern cosmologist would rather use a full reconstruction in three dimensions of the peculiar velocities. Such reconstructions are based on Wiener Filter algorithm, or forward modeling of the data-set and likelihoods depending on the observational data used : galaxy distances or galaxy redshifts. Tragically, very few public releases of 3D peculiar velocity reconstructions are available to date, the largest one being the reconstruction from the redshift survey 2MASS by Lavaux & Hudson (2011). In this article, about 56,000 galaxy distances and 1,000 type Ia supernovae distances (SNIa) from the catalogue CosmicFlows4 (CF4) are used to publicly release 3D reconstructions of the local Universe gravitational field. 100 Mpc. ities (without reconstruction) and derive a measurement of the Local universe bulk Flow, see for example : Dai et al. (2011), Turnbull et al. (2012), Feindt et al. (2013), Boruah et al. (2020), Mohayaee et al. (2021), Peterson et al. (2021). In this article we study galaxy and SNIa distances to deliver a new measurement of the growth rate of structure fσ8 and an analysis at large distance of the bulk flow.

**2. Data and 3D reconstruction **

“The interest of producing 3D reconstructions does not all lie in deriving maps and cosmography of the nearby large scale structures. The grids can be used to test some cosmological hypothesis like the general relativity model for gravity via the growth rate of large-scale structures (see for example Hudson & Turnbull (2012), Dupuy et al. (2019)) and the homogeneity scale of the Universe via a test of the mean of all gravitational velocities enclosed in a sphere, the bulk flow. Both of these cosmology measurements are very sensitive to the number density and to the robustness of the distance moduli used. Since more than a decade, measurement of distances of Type I a supernovae promises to the cosmologist more accuracy on distance moduli at large distance than the classic galaxy distance relations. Already some literature exists that used up to a few hundred supernovae distances to compute their peculiar velochelene. The fourth release of the CosmicFlows catalog (Tully et al. 2022) provides about 56,000 measurements of galaxy distances and about 1,000 Supernovae Ia distance moduli measurements. Such composite catalogs of distances deliver the raw material to compute peculiar velocities. Since the first Cosmic-Flows catalog, our peculiar velocity computational tools have evolved from direct analysis of Malmquist biased radial peculiar velocities (CF1 1,600 galaxies), to Wiener Filter linear 3D reconstructed dataset (CF2 : 8,000 galaxies) that allowed to build some modern cosmography of our Local universe (Courtois et al. 2013), to a forward modeling iterative procedure for the third much larger data-set (CF3: 18,000 galaxies). CF3 was reaching greater distances and was used to uncover distant features like for example the Cold Spot Repeller (Courtois et al. 2017) and the Vela Supercluster (Courtois et al. 2019). The current CF4 data-set is three times larger in number of galaxies than CF3 and is doubling its reach in the northern hemisphere. To be able to handle its 3D reconstruction we are using an iterative forward modelling procedure with a Hamiltonian Monte-Carlo (HMC) algorithm in order to explore some free parameters values (i.e. Ωm, bias, scatter component of the non-linearity in the velocity field solution σNL, …). This procedure is an extension of the procedure used for CF3 catalog and described in Graziani et al. (2019) and Graziani & Rigault (2023) in preparation. The over-density field of full matter (dark +luminous) δm is obtained at the position and time (x,t) through the This procedure is an extension of the procedure used for CF3 catalog and described in Graziani et al. (2019) and Graziani & Rigault (2023) in preparation. The over-density field of full matter (dark +luminous) δm is obtained at the position and time (x,t) through the reconstructed

“3D full matter peculiar( (gravitational) velocity field um by : ∇.um = −aHf(Ωm)δm(x,t) (1) where f is the growth rate of structures which depends on the cosmological parameter Ωm which is a free parameter for the computation, a is a fixed expansion rate and H is an Hubble expansion factor varied iteratively in the HMC for the convergence of the solution. In this article, we use a velocity statistical indicator introduced by Gorski et al. (1989) and noted ψ1. This indicator depends only on radial peculiar velocities. ψ1 is defined as: ψ1(r) = uA · uB (ˆrA · ˆrB)2 = uAuB cosθAB cos2 θAB (2) Dupuy et al. (2019) using the direct radial peculiar velocities of the Cosmic-Flows-3 data-set, found fσ8 = 0.43(±0.03)obs(±0.11)cos.var. out to z=0.05. However, since CF4 is made of several surveys, the computation starts by fitting Gaussian distributions on the distribution of the data in order to compute the starting priors for the likelihood. Figure 1 shows that the catalog contains two classes of supernovae and also two classes of galaxy distances: a class of data with higher accuracy (labelled type 0) with smaller than 0.5 mag errors on distance modulus (in blue) and another class of data with medium accuracy (labelled type 1) with errors on distance modulus larger or equal to 0.5 mag (in green). In this article all computations are made in the ΛCDM cosmological model with initial values of Ωm = 0.3, H0 = 75 km s−1 Mpc−1 and a limitation on the phases reconstructed in Fourier space of kmax =0.1. In order to reach convergence on the parameters, the computation were run over for about 3,700 HMC steps for the supernovae sub-sample and for about 5,800 steps for the CF4 full data-set. The resulting over-density δ and gravitational velocity fields are averaged (after removing the burning steps of the HMC) in order to deliver values on grids with resolutions of 1283 up to z = 0.4 for the supernovae sub-sample…”

(More to come!)