  The standard cosmological model supposes that the dominant matter component
changes in the course of the evolution of the universe. We study the
homogeneous and isotropic universe with non-zero cosmological constant in the
epoch when the dominant matter component has a form of a gas of low-velocity
cosmic strings. It is shown that after the scale transformation of the time
variable such a model and the standard model of a spatially flat universe
filled with pressure-free matter provide the equivalent descriptions of
cosmological parameters as functions of time at equal values of the
cosmological constant. The exception is the behavior of the deceleration
parameter in the early universe. Pressure-free matter can obtain the properties
of a gas of low-velocity cosmic strings in the epoch when the global geometry
and total amount of matter in the universe as a whole obey an additional
constraint. This constraint follows from the quantum geometrodynamical approach
in the semiclassical approximation. In terms of general relativity, its
effective contribution to the field equations can be linked to the evolution in
time of the equation of state of matter caused by the processes of
redistribution of energy between matter components.
