Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-02-28
Class.Quant.Grav. 16 (1999) 2197-2224
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
33 pages with 12 figures. To be published in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/16/7/304
We generalize simplicial minisuperspace models associated with restricting the topology of the universe to be that of a cone over a closed connected combinatorial $3-$manifold by considering the presence of a massive scalar field. By restricting all the interior edge lengths and all the boundary edge lengths to be equivalent and the scalar field to be homogenous on the $3-$space, we obtain a family of two dimensional models that include some of the most relevant triangulations of the spatial universe. After studying the analytic properties of the action in the space of complex edge lengths we determine its classical extrema. We then obtain steepest descents contours of constant imaginary action passing through Lorentzian classical geometries yielding a convergent wavefunction of the universe, dominated by the contributions coming from these extrema. By considering these contours we justify semiclassical approximations based on those classical solutions, clearly predicting classical spacetime in the late universe. These wavefunctions are then evaluated numerically. For all of the models examined we find wavefunctions predicting Lorentzian oscillatory behaviour in the late universe.
da Silva Cristovao Correia
Williams Rosa M.
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