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 <z<2. We show the model parameter distributions in the degenerate higher-order scalar-tensor (DHOST) theory, and its popular subclasses (e.g., Horndeski and GLPV theories).etc. We specify the di↵erences and characteristics of the subclasses in the space of observable quantities for forthcoming galaxy surveys and planned gravitational-wave observations, arguing how to di↵erentiate the theories. In the second part, we consider primordial perturbations with a single inﬂaton ﬁeld in the framework of 4d-Hoˇrava-Lifshitz gravity. For the sake of Lorentz violation in gravity, all the components obey Lifshitz scaling and one additional scalar degree of freedom appears, which is called “Khronon”. The Khronon gravitationally couples to the inﬂaton, but it has been less known how the Khronon behaves in the inﬂationary universe. We show that the curvature perturbation is preserved at super-horizon scales. We demonstrate that the scalar perturbations where Lorentz invariance is explicitly broken are still consistent with cosmological observations whereas the primordial tensor perturbation undergoes a signiﬁcant modiﬁcation of the shape of its power spectrum. As a result, we conclude that testing Lorentz symmetry of the gravity sector at the inﬂationary energy scale is quite possible by a direct measurement of primordial gravitational waves. In the last part, we develop the methodology of testing gravity at high redshifts. We consider the gravitational lensing of the CMB, so-called CMB lensing, by massive radio galaxies, aiming to measure the growth history of the large scale structure at z>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.