CE31 - Physique Subatomique, Sciences de l'Univers, Structure et Histoire de la Terre

Modeling galaxy clustering in the non-linear regime – SPHERES

SPHERES: Modeling the large-scale structure of the Universe in the non-linear regime

Modelling the distribution of matter on cosmological scale thanks to large-deviation theory, application to the case of weak gravitational lensing by the large-scale structure of the Universe, quantification of the information gain and forecasts for future large galaxy surveys.

Applying large-deviation theory to cosmic shear statistics

Future galaxy surveys will map the distribution of galaxies and release gigantic precision datasets. A key issue is therefore to identify a few observables in order to optimally extract cosmological information. Because non-Gaussianities inevitably arise due to the highly non-linear equations of gravity, part of the information is not captured by power spectra but is recorded in higher order statistics. In maximally symmetric configurations (namely when counting galaxies in spheres), largedeviation theory yields analytical predictions with sub-percent precision on mildly non-linear scales where perturbation theory usually breaks down (typically above 10 Mpc/h at redshift z=0). This groundbreaking situation should prove crucial to analyse future galaxy surveys. The goal of this ANR is to develop this approach in the context of weak lensing maps, investigate formal aspects of the theory, apply it to current data, do forecasts for Euclid/LSST and compare the constraining power of counts-in-spheres to standard power spectrum analysis.

The only known observable which can be analytically predicted in the mildly non-linear regime (down to a couple of Mpc scale) is count-in-spheres. The basic idea of these statistics is to focus on highly symmetric configurations (respecting spherical symmetry) where non-linear solutions to the gravitational dynamical equations are known (the so-called spherical collapse model). Highly symmetric configurations then yield very accurate analytical predictions in the mildly non-linear regime, well beyond what is usually achievable using the standard hierarchy of N-point correlation functions. Such a symmetric configuration is fulfilled when counting galaxies in concentric spheres and studying the joint distribution of these concentric galaxy densities.
The reason of that success lies in the identification of a regime of large deviations which allows us to compute the statistics of the final state of the matter distribution in the Universe from the initial conditions knowing that « an unlikely fluctuation is brought about by the least unlikely of all unlikely paths ». In other words, one can identify the most likely dynamics in the Universe (spherical collapse in this context) and assume that this particular path on average dominates the fate of the Universe.
The purpose of this ANR is to develop a consistent and complete framework and go from the theoretical challenges to applications on observational datasets. The three main objectives are to:
- develop counts-in-spheres statistics specifically in the context of weak lensing maps ;
- deepen our understanding of the theory (formal aspects) and propose new methods to extract information from the large-scale structure by means of Gaussianisation and Lagrangian measurements ;
- go from the proof of principle to estimator validation and eventually practical implementations by applying it to current surveys and do forecasts for upcoming experiments such as Euclid.

The main results obtained within the SPHERES team so far are the following:

1) Count-in-spheres applied to cosmic shear: Alexandre Barthelemy (PhD) published a theoretical model for the one-point statistics of the convergence field in the context of weak gravitational lensing (Barthelemy+20a) which notably accounts for the geometry of the past light cone. He successfully compared his calculations to state-of-the-art numerical simulations. Alexandre then added corrections to this theory due to the so-called post-Born effects (Barthelemy+20b) that are usually neglected (geodesic deviations and lens-lens coupling). He showed that these corrections are important for CMB lensing but remain negligible for cosmic shear surveys. Currently, A. Barthelemy implements large-deviation theory in the more realistic (and complex) case of mass mapping where a compensated filter is applied.

2) Forecasts: First promising forecasts with count-in-spheres of the 3D matter density field were obtained in Uhlemann+20 to constrain cosmological parameters with a particular focus on neutrino mass. We showed that this observable could improve significantly the constraints based on power spectrum alone (factor 5 on Om and 2 on s8). The hiring of Aoife Boyle as the ANR postdoc at the end of 2019 allowed us to continue this work since Aoife now works on producing forecasts but now in the case of cosmic shear.

In the next few months, we will continue the ongoing works on the theory of counts in cones for lensing and on producing forecasts. We will also study more formal aspects of the theory: statistics of errors, Gaussianisation and semi-Lagrangian statistics.

1. Barthelemy A., Codis S., Uhlemann C., Bernardeau F. and
Gavazzi R., «Game of cones : a nulling strategy for modelling
lensing convergence in cones with large deviation theory«, 2020,
MNRAS, 492, 3420;
2. Matsubara T. & Codis S., «The large-separation expansion of
peak clustering in Gaussian random fields«, Phys. Rev. D, 2020,
101, 063504;
3. Barthelemy A., Codis S., Bernardeau F. «Post-Born corrections to
the one-point statistics of (CMB) lensing convergence obtained
via large deviation theory«, 2020, MNRAS, 494, 3368;
4. Uhlemann C., Friedrich O., Villaescusa-Navarro F. Banerjee
A., Codis S.,«Fisher for complements: Extracting cosmology and
neutrino mass from the counts-in-cells PDF«, 2020, MNRAS, in
press

Future galaxy surveys will map the distribution of galaxies and release gigantic precision datasets. A key issue is therefore to identify a few observables in order to optimally extract cosmological information. Because non-Gaussianities inevitably arise due to the highly non-linear equations of gravity, part of the information is not captured by power spectra but is recorded in higher order statistics. In maximally symmetric configurations (namely when counting galaxies in spheres), large-deviation theory yields analytical predictions with sub-percent precision on mildly non-linear scales where perturbation theory usually breaks down (typically above 10 Mpc/h at redshift z=0). This groundbreaking situation should prove crucial to analyse future galaxy surveys. The goal of this ANR is to develop this approach in the context of weak lensing maps, investigate formal aspects of the theory, apply it to DES data, do forecasts for Euclid/LSST and compare the constraining power of counts-in-spheres to standard power spectrum analysis.

Project coordinator

Madame Sandrine Codis (Centre National de la Recherche Scientifique - Délégation Régionale Ile de France Gif-Sur-Yvette)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

IAP Institut d'astrophysique de Paris
CNRS - DR04 Centre National de la Recherche Scientifique - Délégation Régionale Ile de France Gif-Sur-Yvette

Help of the ANR 396,413 euros
Beginning and duration of the scientific project: November 2018 - 48 Months

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