Mathematics – Logic
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........37d&link_type=abstract
Thesis (PH.D.)--TUFTS UNIVERSITY, 1990.Source: Dissertation Abstracts International, Volume: 51-06, Section: B, page: 2937.
Mathematics
Logic
1
Scientific paper
We describe the modern approach to quantum cosmology initiated primarily by Hartle and Hawking and by Vilenkin. The results of this approach culminated with the "no-boundary" and the "tunneling" boundary conditions of the wave function of the Universe. This thesis mainly deals with the latter one. The tunneling wave function of the Universe is not always similar to a wave function describing usual quantum - mechanical tunneling. The differences are illustrated using the example of a homogeneous anisotropic minisuperspace model (which is also of interest in its own right). The tunneling wave function of the model is found in the limit of small and large anisotropy. The tunneling wave function is also calculated for an inflationary cosmological model with a variable gravitational "constant". The resulting probability distribution for the initial states of the Universe is peaked at the highest maximum of the effective potential V = V max, with the initial value of the Planck mass m_sp{P }{(0)} ~ V _sp{Max}{1/4}. The initial states predicted by the tunneling wave functions are exactly the states needed for a long inflation. This is in contrast to the "no-boundary" proposal of Hartle and Hawking which gives a probability distribution which is incompatible with inflationary scenario.
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