Previously to current work, I worked on a class of field theoretic models which produce an open (less than critical matter density) universe. (A poster on this (1.1Mb) is here.) Current observations (e.g. of the CMB, the cosmic microwave background) show a large degree of homogeneity, but are as yet inconclusive about spatial curvature (flat, open or closed). Most theories producing a homogeneous and isotropic universe rely upon inflation, where the scale factor for the universe accelerates and inhomogeneities are diluted away. Requiring sufficient inflation to homogenize random initial conditions also drives the universe to very close to critical density, making it almost flat. In 1994, Bucher, Goldhaber and Turok, using earlier work of Gott and Coleman and de Luccia, proposed a model for an open universe where a bubble nucleated in the universe after inflation had begun. The interior of the bubble is an open universe. They demonstrated that a zero radius thin wall bubble (which they proved was a consistent approximation) produces scalar density perturbations consistent with current CMB observations. There is also extensive related work by Yamamoto, Tanaka and Sasaki.

Bubble nucleation in these models occurs in a vacuum, but the presence of a curvature scale and the structure of de Sitter space introduces many subtleties. Comprehensive calculations of the spectrum for the coupled gravity and scalar theories has recently been done for some cases by Garriga, Montes, Sasaki and Tanaka. A recent one field toy model was proposed by Linde. Hawking and Turok proposed a controversial mechanism in early 1998, where the universe tunnels, but not from a false vacuum. In these models the homogeneity in the universe comes from the universe taking the most likely (and hence most symmetric) configuration, as in the Hartle Hawking formulation of quantum cosmology. Linde has suggested using this idea but in the context of the tunneling wave function of the universe. Density perturbations in some of these models have been calculated by various groups, but the interpretation of these models is still controversial, and several authors have contributed suggestions, criticisms and improvements.

Upcoming CMB observations should be able to determine whether the universe has spatial curvature or not. Features in the CMB spectrum will be observed at smaller angles on the sky if the universe is open, due to geodesic divergence. That is, light rays with sources a fixed distance apart in the past, e.g. when the CMB formed, will subtend a smaller angle on the sky today in an (open) curved space, compared to the case where space is flat. This is the same geometrical effect that makes the angles in a triangle on a sphere (a closed curved space) add up to more than 180 degrees, and those on a (open) curved saddle add up to less than 180 degrees.

I have calculated perturbations in some of the above models, including a calculation of gravity waves with Martin Bucher. In addition, in order to better understand the field theory of these spaces, David Kaiser and I studied properties of supercurvature modes, which are particular to open universes.

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