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

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

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