Testing the theory of gravity with DESI: estimators, predictions and
  simulation requirements
  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 sometimes questioned in the shadow 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
estimators 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 estimators
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 and to better understand the impact of key systematic
effects. Using these, we identify future simulation and analysis needs for
gravity tests using DESI.
