  We consider different scenarios of the evolution of the universe, where the
singularities or some non-analyticities in the geometry of the spacetime are
present, trying to answer the following question: is it possible to conserve
some kind of notion of particle corresponding to a chosen quantum field present
in the universe when the latter approaches the singularity? We study scalar
fields with different types of Lagrangians, writing down the second-order
differential equations for the linear perturbations of these fields in the
vicinity of a singularity. If both independent solutions are regular, we
construct the vacuum state for quantum particles as a Gaussian function of the
corresponding variable. If at least one of two independent solutions has a
singular asymptotic behavior, then we cannot define the creation and the
annihilation operators and construct the vacuum. This means that the very
notion of particle loses sense. We show that at the approaching to the Big Rip
singularity, particles corresponding to the phantom scalar field driving the
evolution of the universe must vanish, while particles of other fields still
can be defined. In the case of the model of the universe described by the
tachyon field with a special trigonometric potential, where the Big Brake
singularity occurs, we see that the (pseudo) tachyon particles do not pass
through this singularity. Adding to this model some quantity of dust, we
slightly change the characteristics of this singularity and tachyon particles
survive. Finally, we consider a model with the scalar field with the cusped
potential, where the phantom divide line crossing occurs. Here the particles
are well defined in the vicinity of this crossing point.
