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It is shown that the initial conditions in the quasi-Heisenberg quantizationscheme can be set at the initial cosmological singularity per se. Thispossibility is provided by finiteness of some quantities, namely momentums ofthe dynamical variables, at a singularity, in spite of infinity of thedynamical variables themselves. The uncertainty principle allows avoiding anecessity to set values of the dynamical variables at singularity, as a wavepacket can be expressed through the finite momentums. Influence of the initialcondition set in the singularity in such a way to a number of gravitons under avacuum state, arising during later evolution, is investigated. It is shownthat, even choosing of some special state at the singularity minimizing latetime expansion rate, some amount of gravitons still appear in the late timeevolution.

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