  We account for the interaction of the Bose-condensed fraction with the normal
phase in an effective dynamical equation such as the Gross-Pitaevskii equation.
We show that the low-energy excitations can be treated as sound waves with
speed dependent on the condensate density. This allows us to reduce the problem
to the calculation of the determinant of the Laplace operator on a curved space
and apply standard methods of quantum gravity to get the leading logarithmic
contribution of the determinant. This produces the first quantum correction due
to the noncondensed fraction to the Gross-Pitaevskii equation for the
condensate. The correction describes an additional quantum pressure in the
condensate and evaporation-condensation effects.
