In order to understand why the Universe has the structure observed in galaxy surveys and how this structure evolves, one must know its initial state. Since 2012, a collaboration of cosmologists from France, the United Kingdom and Germany has been working on this issue. Using advanced computer modelling techniques, the research team has succeeded in translating the distribution of galaxies, observed by the Sloan Digital Sky Survey, into detailed maps of the initial state of the Universe, of dark matter streams and their velocities. These maps are now publicly available online.


The cosmic web: the present-day structure of the Universe

At the largest scales in our Universe, matter is organised in a complex network of sheets and filaments delineating large empty regions, the voids: the filaments connect the densest regions of the Universe, where galaxies cluster; the whole of this network is called the cosmic web. It is made of dark matter, a substance of yet unknown nature that makes up more than 80% of the total mass of the Universe. As it does not emit light nor interact with luminous matter, its distribution and evolution are not directly observable and must be inferred. Galaxies are part of the luminous component of matter, and form in regions where dark matter is concentrated. The clustering of galaxies thus traces the underlying structure of dark matter.

How did structure appear in the Universe? In order to discover the origin of complexity in a system, physicists generally resort to experimentation: they define initial conditions, and then observe how the system evolves. But how to answer such a question in cosmology, that is to say when the system studied is the Universe as a whole? As experimentation is not possible, the technique of “numerical simulations” provides some elements of answer. Starting from initial conditions in which dark matter exhibits density fluctuations, that is to say an alternation of denser and less dense regions, simulations show that the overall matter field evolves under the gravitational attraction generated by the densest dark matter regions, and that galaxies then appear and cluster in these regions. These predictions are in qualitative agreement with observations, but they do not provide information on the initial conditions to be used in order to reproduce the observed Universe. It is by knowing the initial conditions of which it is the product, that one one can understand the origin of the large-scale structure in our Universe.

The reconstruction of the initial conditions

Imagine for a moment that we had infinite computational power at our disposal. The best thing to do would then be to try all the possible initial conditions for the Universe, to run a numerical simulation for each of them, and to compare the result to observations. The simulations that would most closely resemble the data would be adopted as a representation of the entire history of this region of the Universe through cosmic ages. Unfortunately, this scenario is not possible because current computing resources are far from sufficient. However, thanks to powerful statistical methods, the mathematical foundation of which has been derived only thirty years ago, it is now possible to focus on exploring only the plausible initial conditions, avoiding wasting time simulating maps that fail to reproduce currently available observations. To this end, an advanced software called BORG (Bayesian Origin Reconstruction from Galaxies) was developed at the IAP by Jens Jasche and Benjamin Wandelt between 2012 and 2015. Guilhem Lavaux joined the collaboration in 2014 to significantly increase some aspects of the model and performance.

In his thesis, Florent Leclercq, PhD student at the IAP between 2012 and 2015, applied the BORG software for the first time to a cosmological survey, the Sloan Digital Sky Survey (SDSS) main galaxy sample. For several hundreds of thousands of galaxies, this catalog provides their position on the sky, as well as their redshift; the latter results from the combination of the distance of each galaxy to the Milky Way and its peculiar velocity in the streams of matter. Using BORG, it has been possible to reconstruct all the initial conditions that are compatible with the observations in the volume covered by these galaxies, up to a distance of about 2 billion light-years from the Milky Way. This work required nearly a year of calculations on the IAP supercomputer, Horizon. Figure 1 shows one scenario among all the possible cosmic histories, in which the distribution of dark matter evolves through the ages under the effect of gravity to reproduce the cosmic web as observed by the SDSS.

Figure 1Figure 1: A possible scenario for the emergence of large structures in the Universe: the dark matter field evolves from its initial conditions through cosmic ages (from left to right), until the present time (right panel). The different panels show the density of dark matter at a time of cosmic evolution characterized by the parameter a, the relative size of the Universe at that time compared to its size today. Light areas correspond to places where dark matter density is low, and dark areas to where it is high. At the present time (right panel), the structure of the dark matter field exactly matches the distribution of galaxies observed by the SDSS, shown as red dots. The Milky Way is located in the lower left corner of each map, at the lower tip of the triangle of galaxies shown in red, with coordinates [0,0] (Source: Jasche et al. 2015, Journal of Cosmology and Astroparticle Physics).

The dark matter streams

The availability of the initial conditions of our cosmic neighborhood reveals a wealth of new information about dark matter. Using tools developed for numerical simulations, the researchers have been able to produce maps of velocity fields in observations, indicating the direction and strength of the streams of matter at each point. Figure 2 shows how the streams of matter approach and move away from us. The Sloan Great Wall, one of the largest structures in the known Universe, is clearly visible in the center of the diagram, at the intersection of convergent dark matter streams coming from the front and the back of the plane defined by this wall of galaxies.

These maps are accurate even in regions of low galaxy density, where the reconstruction is difficult because the data are not very informative. Until now, only the velocities of individual galaxies were accessible in observations, at the cost of heavy campaigns of complementary observations and calibration of the measurements used to deduce these velocities. Note that in both Figure 1 and Figure 2, the large-scale structure is well-constrained in the regions sampled by the observed galaxies, but outside, the reliability of the depicted density and velocity fields decreases with the distance to the galaxy survey boundaries.

All the maps produced by the research collaboration during this project have been made publicly available. They are at the disposal of the scientific community for further studies, for example to analyze the formation and properties of galaxies as a function of their environment.

Figure 2Figure 2: Distance cone along the celestial equator, showing the radial component of the velocity field (in kilometers per second) as a function of distance[1] from the Milky Way (at the tip of the cone). The slice has a constant thickness of about 3 megaparsecs[1] (or 9 million light-years) at all distances. In blue regions, matter is moving towards us, and in red regions it is moving away from us. The galaxies of the Sloan Digital Sky Survey main sample are shown as black dots. In the center of the image, the infall of matter on the Sloan Great Wall, one of the largest structures of the known Universe, can be observed at the interface between the two big red and blue crescents (at about 220 megaparsecs), the former showing matter in the foreground of the wall falling on it while flying away from the Milky Way, the latter showing matter in the background of the wall falling on it while getting closer to the Milky Way (Source: Leclercq et al. 2017, Journal of Cosmology and Astroparticle Physics).

Accessing the initial conditions and the dynamics of dark matter from galaxy surveys opens up new ways of assessing the validity of theoretical models in light of observations. Applying these techniques to the next-generation deep surveys of galaxies, such as the one from the Euclid satellite, the Dark Energy Spectroscopic Instrument, or the Large Synoptic Survey Telescope, will allow unprecedented tests of the current paradigm of cosmic web formation and evolution.

This research was supported by funding from the European Research Council (ERC grant 614030, “Darksurvey”), from the “Agence Nationale de la Recherche” (ANR-10-CEXC-004-01), from the “Labex Institut Lagrange de Paris” (ANR-10-LABX-63, ANR-11-IDEX-0004-02), from the Alexander von Humboldt foundation and the “Cluster of Excellence”, from the “Deutsche Forschungsgemeinschaft” (German Research Foundation, “Origin and Structure of the Universe”).

[1] Distances are indicated in megaparsecs (corresponding to about 3 million light-years), and were calculated for a value of the Hubble constant, measuring the expansion rate of the Universe, of 100 km/s/megaparsec. For the actually measured value of about 70 km/s/megaparsec, one must divide the indicated distances by 0.7.


puce The article in the Monthly Notices of the Royal Astronomical Society : Jasche, Wandelt, 2013, « Bayesian physical reconstruction of initial conditions from large scale structure surveys » https://academic.oup.com/mnras/article/432/2/894/1020272 (version publique)

puce The article in the Journal of Cosmology and Astroparticle Physics : Jasche, Leclercq, Wandelt, 2015, « Past and present cosmic structure in the SDSS DR7 main sample » http://iopscience.iop.org/article/10.1088/1475-7516/2015/01/036 (version publique)

puce The article in the Journal of Cosmology and Astroparticle Physics : Leclercq, Jasche, Lavaux, Wandelt, Percival, 2017, « The phase-space structure of nearby dark matter as constrained by the SDSS » http://iopscience.iop.org/article/10.1088/1475-7516/2017/06/049 (version publique)

puce Florent Leclercq's PhD thesis (Université Pierre et Marie Curie) : « Bayesian large-scale structure inference and cosmic web analysis » http://florent-leclercq.eu/phd.php

puce Maps and software from the BORG analysis of the SDSS : http://florent-leclercq.eu/data.php


Web editing and layout: Valérie de Lapparent

February 2018

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