Abstract
This thesis aims to explore and emphasise on the significant relativistic contributions to observable galaxy number counts. We start by mathematically proving the frame-invariance of galaxy number counts in Einstein and Jordan frames in the second chapter, and then move on to computing the full-sky correlation function and power spectrum including all relativistic effects in the third chapter. The fourth chapter deals with modelling of the angular power spectra in the redshift space and also accounts for the intermediately nonlinear regime. In the fifth and sixth chapters, we establish the importance of including lensing corrections to the main signal of probes such as galaxy-galaxy lensing, and for measurements in case of tests of gravity like $E_g$ statistics, respectively. Finally, we also talk about the shape and size correlations of galaxies occurring as a part of weak lensing data, arising out of the phenomenon of intrinsic alignment.
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