Towards testing the theory of gravity with DESI: summary statistics, model predictions and future simulation requirements

Abstract

Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for — its applications on those scales being largely based on extrapolation and its validity there sometimes questioned in the shadow of the discovery of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of N-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel summary statistics beyond linear redshift distortions in two well-studied modified gravity models — chameleon f(R) gravity and a braneworld model — and the potential of testing these deviations from GR using DESI. These summary statistics employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey (by matching the volumes and galaxy number densities of the mocks to those in the real survey) and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI.

Large-scale dark matter simulations

“…However, departures from GR on cosmological scales are still possible and have received significant attention as a potentially important piece to understand the accelerated expansion of the Universe. In fact, testing gravity on cosmological scales is one of the primary science goals of the upcoming generation of large-scale structure observations and gravitational wave detectors (Alam et al 2021;Belgacem et al 2019).…”

Testing modified gravity theories with marked statistics

“…We have reviewed the analytical study of marked statistics that up-weight low density regions in the Universe. [16][17][18][19] The idea behind marked statistics is to assign a value (the mark) to each entity in a catalogue and perform statistics over the resulting weighted objects. An efficient way to suppress non-linearities is by choosing a mark that gives more weight to objects that reside in low density regions, which become less important as one consider higher density regions.…”

“…Other authors working with simulations have used different parameters and mark functions. 18,[26][27][28] (3) Weight the density field of tracers 1 + δ X (x) with the mark function m(δ(x), R) to obtain the marked density field…”

Fast generation of mock galaxy catalogues in modified gravity models with COLA

“…We use a full N-body simulation suite called elephant, which was introduced and validated in [37], to benchmark the results of our runs based on COLA. The elephant suite was produced using ecosmog [19], a MG extension of the adaptive mesh refinement code RAMSES [38] that solves the exact equations for the fifth force; these simulations were recently used to create mock galaxy catalogues in [2,39,40] 3 . Table 1 describes the parameters of the suite such as the box size, the mass resolution and the gravity models implemented, and the cosmological parameters employed are:…”

“…It is crucial to make accurate theoretical predictions of the properties of the LSS on non-linear scales to successfully constrain the gravity model (see e.g. [2]). This can be achieved by means of cosmological simulations, but O(10 3 ) realisations must be produced to match the volume of Stage IV surveys and compute an accurate estimate of the covariance matrices.…”