Strength of singularities in varying constants theories
  In this paper we consider a specific type of the bimetric theory of
gravitation with the two different metrics introduced in the cosmological
frame. Both metrics respect all the symmetries of the standard FLRW solution
and contain conformally related spatial parts. One of the metric is assumed to
describe the causal structure for the matter. Another metric defines the causal
structure for the gravitational interactions. A crucial point is that the
spatial part of the metric describing gravity is given by the spatial part of
the matter metric confromally rescaled by a time-dependent factor $\alpha$
which, as it turns out, can be linked to the effective gravitational constant
and the effective speed of light. In the context of such a bimetric framework
we examine the strength of some singular cosmological scenarios in the sense of
the criteria introduced by Tipler and Kr\'olak. In particular, we show that for
the nonsingular scale factor associated with the matter metric, both the
vanishing or blowing up of the factor $\alpha$ for some particular moment of
the cosmic expansion may lead to a strong singularity with infinite value of
the energy density and infinite value of the pressure.
