SINGULARITIES AND THEIR CROSSING IN GRAVITY AND COSMOLOGY

We discuss the problem of singularity crossing in isotropic and anisotropic universes. First, we consider the so called soft or sudden singularities and, in particular the Big Brake singularity. This singularity was discovered in a particular tachyon cosmological model and it was also shown that this kind of singularity arises in a very simple model, where matter is represented by the anti-Chaplygin gas. At the the encounter with the Big Brake singularity the universe has a finite scale factor, a vanishing expansion velocity and an infinite deceleration. The Christoffel symbols also vanish the geodesics are regular and the universe easily can cross such a singularity. Adding to the anti-Chaplygin gas or to the tachyon matter some amount of dust we see that the Big Brake singularity is substituted by a more general soft singularity, its crossing implies a certain transformation of the properties of matter. The crossing of the Big Bang – Big Crunch singularity is more counter-intuitive. However, we describe it for both Friedmann universe and Bianchi-I universe using the field reparametrization of the variables present in models (a scalar field and the metric). Then we consider the Wheeler-DeWitt equation and show that the probability for the universe to find itself at the soft singularity is different from zero, while the encounter with the Big Bang – Big Crunch singularity is suppressed. We analyze the possibility to construct Fock spaces of quantum particles at the vicinity of different cosmological singularities and see when it is possible and when it is not possible. Finally, we present some attempts to develop general approach to the connection between the field reparametrization and the elimination of singularities.