Testing General Relativity with the next generation of cosmological surveys

The late-time acceleration expansion of the Universe is conceptually considered the great burdensome issue in theoretical physics (cosmological problem) dubbed dark energy (DE) problem. In general relativity (GR) framework view point, there are two ways to explain where this acceleration might originate from; this riddle might either emerge from some unknown dark energy models or general relativity is a mistake on cosmological scale and dark energy is insubstantial. Innovative efforts have been carried out to comprehend the origin of the cosmic acceleration, involving surveys such as baryon acoustic oscillations (BAOs), Type Ia supernovae, weak gravitational lensing and the abundance of galaxy clusters. The next generation of cosmological surveys including LSST, DES, eBOSS, DESI, PFS, SKA and WFIRST; are aimed to provide percent-level or higher measurement of history of expansion and growth of structure over a volume which is sizable fraction of the whole observable Universe, these measurements provides strong constrains on DE. In this analysis, we investigate the Horndeski scalar-tensor theories and beyond which has been recently described in the generilized dark energy (DE) or scalar-tensor paradigm - dubbed unified dark energy (UDE). This applies the 3+1 Arnowitt-DeserMisner (ADM) formalism where a general action in unitary gauge depends on the lapse function and geometrical scalar quantities. This approach is convenient since it generates a unified framework of modified theories based on UDE or effective field theory (EFT) of linear cosmological perturbations on Friedmann-Lemaitre-Robertson-Walker (FLRW) background, this are generally characterized by five free time-dependent functions αi (αB,αH,αK,αM,αT ) each describing different properties of unified dark energy physical outcome. The evolution equations for the given UDE which assimilates beyond-Horndeski paradigms appear to correspond to a non-conservative DE scenario, in which the total energy-momentum tensor is not conserved. Furthermore, we evaluate the large-scale imprint of this UDE, by probing the two-point correlation function or power spectrum of galaxy number counts and the magnification of galaxies, on horizon scales; making sure to include the full relativistic corrections in the observed overdensity and convergence. This yield new observables which gives independent insights regarding the peculiar velocity of galaxies, the growth of structure of the Universe etc