The quest for dark energy (DE) in the universe is central to modern cosmology. Whether in the form of a cosmological constant, an exotic form of matter or the consequence of a modified theory of gravity (MG), its nature still remains unknown. The goal of the ProGraceRay project is to build robust probes of gravity by focusing on the impact of the relativistic physics of light on cosmological observables of the clustering of matter. Photons do not travel along straight-lines. Moreover their energy is not only governed by the expansion of the Universe but also by large-scale structures. Our usual view of the Universe is therefore distorted by two well-known effects. First, the angular positions, shapes, sizes and orientations of sources are changed (as well as their luminosity) due to Weak gravitational Lensing (WL). Second, the radial position of galaxies is modified due to redshift perturbations, resulting in a global change of the apparent distribution of galaxies along the line-of-sight called Redshift Space Distortions (RSD). These two effects blur the original signal. However, what may be considered as a problem is in fact an advantage since these effects carry key information on the metric along the line-of-sight (WL), the velocities and potential of the sources (RSD). Many (uncontrolled) approximations are often used in current studies to account for these effects. However (often-neglected) non-trivial relativistic effects can contribute at the 1 to 10% level in WL and standard RSD analyses, at the 1% to 50% level in galaxy-galaxy lensing and at the 100% level to the dipole of the galaxy cross-correlation. Moreover, studies based on numerical simulations as well as analytical models usually focus on WL or RSD separately (pertaining to two different communities). However, in the context of MG, combining WL and RSD is necessary, since they can disentangle the two metric potentials. The ProGraceRay project will build on the complementary expertise of its participants: WL&RSD, cosmological scales&galactic scales, theory&simulations, statistics&systematics. We will advance the field through the realization of the world largest MG N-body simulations using the RAMSES code. These will accurately compute the matter distribution in the Universe for a wide range of MG models. Dark matter halos will then be populated with galaxies by calibrating the halo-galaxy relation in dedicated hydrodynamical simulations in MG, which will provide accurate ab-initio catalogs. Instead of the usual approximations, the proposal exploits the uniqueness of our ray-tracing algorithm that solves billions of geodesic equations at the same level of resolution as the dynamical code. The resulting catalogs will naturally include for the first time all the relativistic effects under the weak-field approximation for various MG models. They will cover large volumes similar to near-future surveys from the linear regime down to the non-linear regime of structure formation. We will investigate the impact of relativistic effects and MG on the 1, 2, and 3 points statistics of the apparent galaxy distribution (RSD), as well as of the convergence and shear field (WL). These effects will be compared to observational systematics so as to find the best strategies to detect them. Thanks to the galaxy catalogs we will develop analytical models and emulator algorithms that will be provided to the community. These tools will enable quick and accurate predictions of relativistic cross-correlations in MG models. The realization of such an ambitious project can only be made possible with the support of postdoctoral researchers as well as the acquisition of additional computing/storage devices. A major impact is expected since the developed tools can be directly used by the large observational Consortia to constrain the nature of dark energy and gravity thanks to the ongoing and near-future surveys (DESI, Euclid, LSST).