Quantum mechanics allows setting initial conditions at a cosmological singularity: Gowdy model example

Abstract

It is shown that the initial conditions in the quasi-Heisenberg quantization scheme can be set at the initial cosmological singularity per se. This possibility is provided by finiteness of some quantities, namely momentums of the dynamical variables, at a singularity, in spite of infinity of the dynamical variables themselves. The uncertainty principle allows avoiding a necessity to set values of the dynamical variables at singularity, as a wave packet can be expressed through the finite momentums. Influence of the initial condition set in the singularity in such a way to a number of gravitons under a vacuum state, arising during later evolution, is investigated. It is shown that, even choosing of some special state at the singularity minimizing late time expansion rate, some amount of gravitons still appear in the late time evolution.