Studies in inhomogeneous cosmological models

Approaches to cosmology where fewer assumptions are made need to be explored. In this thesis, a theoretical framework is developed where, given a spacetime one can determine what possible non-conducting fluids can generate it. This question is explored for a restricted class of spacetimes but which includes many cases of interest. The fluid velocity field is uniquely determined by the condition of zero energy flux. It is written out explicitly for canonical types of coordinates. Invariant necessary conditions for a perfect fluid are derived. In some cases these are also sufficient. Using these conditions, an algorithmic procedure which delineates possible physical interpretations of a spacetime is developed. It is shown how a generic degenerate case arises. Another framework is developed where observations can be used within spherical inhomogeneous generalizations of Friedmann's models. Observational non comoving coordinates are used so the null geodesic equation is solved by construction. Use of comoving coordinates leads to a particular static solution not suitable for a cosmological model. An inhomogeneous dust model in non-comoving observational spherical coordinates is given by a metric along with constraint equations. We set up a fitting procedure where inhomogeneous observations can be introduced to integrate explicitly Einstein's equation. In this procedure the non commutation problem between spatial averaging of inhomogeneities and Einstein's equations is avoided. This approach is interesting because part of the model is explicitly built based on the observed inhomogeneities. In view of the considerable algebra involved in studies of inhomogeueous models we developed two new tools: GRDB, a sophisticated online database; GRSource, a program that implements the framework for identifying spacetime source fluids. These use the computer algebra system GIMnsor. Finally, stability of spherically symmetric thin shells and wormholes is examined. This work applies to a generalization of the inhomogeneous cosmological models of Einstein and Strauss. It is shows how the existence of a domain wall dominates the landscape of possible equilibrium configurations. It is found that the inclusion of a discontinuous cosmological constant (irrespective of its sign) across the shell affects the stability profiles while a continuous one does not.