1 research outputs found
Wave function of the Universe in the early stage of its evolution
In quantum cosmological models, constructed in the framework of
Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its
further expansion is described as a tunneling transition through an effective
barrier between regions with small and large values of the scale factor at
non-zero (or zero) energy. The approach for describing this tunneling consists
of constructing a wave function satisfying an appropriate boundary condition.
There are various ways for defining the boundary condition that lead to
different estimates of the barrier penetrability and the tunneling time.
In order to describe the escape from the tunneling region as accurately as
possible and to construct the total wave function on the basis of its two
partial solutions unambiguously, we use the tunneling boundary condition that
the total wave function must represent only the outgoing wave at the point of
escape from the barrier, where the following definition for the wave is
introduced: the wave is represented by the wave function whose modulus changes
minimally under a variation of the scale factor . We construct a new method
for a direct non-semiclassical calculation of the total stationary wave
function of the Universe, analyze the behavior of this wave function in the
tunneling region, near the escape point and in the asymptotic region, and
estimate the barrier penetrability. We observe oscillations of modulus of wave
function in the external region starting from the turning point which decrease
with increasing of and which are not shown in semiclassical calculations.
The period of such an oscillation decreases uniformly with increasing and
can be used as a fully quantum dynamical characteristic of the expansion of the
Universe.Comment: 19 pages, 21 files for 10 EPS figures, LaTeX svjour style. The Sec.2
(formalism of Wheeler-De Witt equation) is reduced. In Sec.3.1 definition of
the outgoing wave from barrier is defined more accurately. In Sec.4.1
semiclassical calculations of wavew function and penetrability are performed
and comparison with results in fully quantum approach is adde