  We consider the effects of graviton multiplet fields on transitions between
string gas phases. Focusing on the dilaton field, we show that it may obstruct
transitions between different thermodynamic phases of the string gas, because
the sign of its dimensionally reduced, $T$-duality invariant, part is conserved
when the energy density of the universe is positive. Thus, many interesting
solutions for which this sign is positive end up in a future curvature
singularity. Because of this, some of the thermodynamic phases of the usual
gravitating string gases behave like superselection sectors. For example, a
past-regular Hagedorn phase and an expanding FRW phase dominated by string
momentum modes cannot be smoothly connected in the framework of string
cosmology with positive sources. The singularity separates them like a
geometric precipice in the moduli space, preventing the dynamics of the theory
from bridging across. Sources which simultaneously violate the positivity of
energy and NEC could modify these conclusions. We provide a quantitative
measure of positivity of energy and NEC violations that would be necessary for
such transitions. These effects must dominate the universe at the moment of
transition, altering the standard gas pictures. At present, it is not known how
to construct such sources from first principles in string theory.
