Homogeneous and some inhomogeneous cosmographic implications of pantheon+ supernova data; and more considerations of inhomogeneity effects in cosmology

In this thesis, we revisit/reinterpret/extend the model-independent analysis method (which we now call spread - luminosity distance fitting, spread-LDF) from our previous work. We apply it to the updated supernova type Ia catalogue, Pantheon+ and recent GRB compilations. The procedure allows us, using only FLRW assumption, to construct good approximations for expansion history of the universe, re-confirming its acceleration to be a robust feature. When we also assume General Relativity, we can demonstrate, without any matter/energy model in mind, the need for (possibly nonconstant) dark energy ("GDE"). We find hints for positive pressure of GDE at z > 1. We extend the use of the spread-LDF method to a particular class of radially inhomogeneous models, in which we can show that observations allow decelerating expansion. Further, we were able to modify the spread-LDF method to be used in Buchert's averaging formalism over cosmic inhomogeneities and the effective FLRW framework derived from it, showing how the observations can be analyzed in terms of the averaged quantities and the corresponding backreaction term can be estimated. The LDF procedure also leads to the possibility of re-coordinatizing the FLRW spacetime such that the relevant metric function is a direct observable. Finally, we present an interesting example of a spacetime, which is inhomogeneous, dynamic but in a steady-state.