Mathematics – Logic
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........39d&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF CONNECTICUT, 1990.Source: Dissertation Abstracts International, Volume: 51-08, Section: B, pag
Mathematics
Logic
2
Scientific paper
Although the Friedmann-Robertson-Walker big bang model explains most features of cosmological observations quite well, it does not represent the complete and final answer to our search for an understanding of the structure of the universe. There is a number of problems which the model fails to resolve, or which the model creates by itself. The most prominent of such problems are the entropy, flatness and horizon problems. All three problems have their roots in assuming exact homogeneity and isotropy for all stages of cosmological evolution, and may potentially be solved by introducing inhomogeneity during the earlier evolution of the universe. The Einstein equations oblige the source of gravity in the standard Friedmann cosmology to be a perfect fluid because of the assumed maximal symmetry in 3-space. When inhomogeneous and/or anisotropic models are studied, however, such an obligation does not exist. It is thus sensible to study the effects of more realistic dissipative fluids as the universe at early times is hot and processes such as the strong interactions of particles can give rise to dissipative processes. Presented in this dissertation are some studies on spherically symmetric inhomogeneous models of the universe with the source of gravity being in the form of an imperfect fluid. Firstly, the Einstein equations with an imperfect fluid energy-momentum tensor which includes some or all of the dissipative contributions are solved. Secondly, the physical properties of the solutions so obtained, in particular the entropy production and the causal structure in connection with the horizon problem, are studied. An asymptotic condition is imposed on the solutions such that the universe evolves from an inhomogeneous state to the current homogeneous and isotropic Robertson-Walker state in order to be in accordance with current observational facts. The solutions are found to have increasing entropy density and thus can solve the entropy problem. Similarly, models built on some of these solutions are found not to have any horizon and flatness problems. Thus all of the standard model problems are potentially solved in our work.
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