Framework for testing the fundamental principles in gravitation and cosmology

In this thesis, we consider how in practice fundamental principles can be constrained by cosmological surveys, mainly by considering popular modifications of Einstein’s general relativity. We specifically investigate (1) breaking the equivalence principle in the generalised scalar-tensor gravity and its observational consequences, (2) the validity of Lorentz invariance in the inflationary universe, and (3) practical observations for testing gravity by CMB lensing data. In the first part, we investigate the parameter distributions of viable generalised scalar-tensor theories with conventional dust matter. We numerically construct the models consistent with the observed Hubble parameter in the redshift range, 0 1. We construct all-sky data of radio surveys and develop the method of how we properly assign the redshift distribution and bias of radio sources. We identify redshift information as the main diculty for the extraction of the growth history of large scale structure from the existing data of galaxy and radio surveys, and CMB lensing, discussing possible improvements in future radio and galaxy surveys. In conclusion, we discuss the levels of violation of fundamental principles in gravitation and cosmology that might be detectable in future observations.