209 research outputs found
Can the scale factor be rippled?
We address an issue: would the cosmological scale factor be a locally
oscillating quantity? This problem is examined in the framework of two
classical 1+1-dimensional models: the first one is a string against a curved
background, and the second one is an inhomogeneous Bianchi I model. For the
string model, it is shown that there exist the gauge and the initial condition
providing an oscillation of scale factor against a slowly evolving background,
which is not affected by such an oscillation "at the mean". For the
inhomogeneous Bianchi I model with the conformal time gauge, an initially
homogeneous scale factor can become inhomogeneous and undergo the nonlinear
oscillations. As is shown these nonlinear oscillations can be treated as a
nonlinear gauge wave.Comment: 10 pages, 5 figure
Cosmological singularity as an informational seed for Everything
It is shown how to place some amount of matter into the cosmological
singularity and to encode its state. A free and massless scalar field is
considered, as a prototype of matter. Two different but coherent approaches to
this issue are presented. The expression for the spectral energy density of the
scalar particles, which is initially encoded at the singularity, is deduced. An
informational aspect of the problem is discussed.Comment: 15 pages, 2 figure
Solution of the discrete Wheeler-DeWitt equation in the vicinity of small scale factors and quantum mechanics in the space of negative constant curvature
The asymptotic of the solution of the discrete Wheeler-DeWitt equation is
found in the vicinity of small scale factors. It is shown that this problem is
equivalent to the solution of the stationary Schr\"{o}dinger equation in the
(super) space of negative constant curvature. The minimum positive eigenvalue
is found from which a continuous spectrum begins.Comment: 8 page
Quantization of the inhomogeneous Bianchi I model: quasi-Heisenberg picture
The quantization scheme is suggested for a spatially inhomogeneous 1+1
Bianchi I model. The scheme consists in quantization of the equations of motion
and gives the operator (so-called quasi-Heisenberg) equations describing an
explicit evolution of a system. Some particular gauge suitable for quantization
is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero
scale factor and it is used to construct a space, where the quasi-Heisenberg
operators act. Spatial discretization as a UV regularization procedure is
suggested for the equations of motion.Comment: 10 page
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