  Manifestations of fluctuating Cooper pairs formed by electrons and holes
populating opposite surfaces of a topological insulator film in the Coulomb
drag effect are considered. Fluctuational Aslamazov-Larkin contribution to the
transresistance between surfaces of the film is calculated. The contribution is
the most singular one in the vicinity of critical temperature $T_\mathrm{d}$
and diverges in the critical manner as $(T-T_\mathrm{d})^{-1}$. In the
realistic conditions $\gamma\sim T_\mathrm{d}$, where $\gamma$ is average
scattering rate of electrons and holes, Aslamazov-Larkin contribution plays
important role and can dominate the fluctuation transport. The macroscopic
theory based on time-dependent Ginzburg-Landau equation is developed for
description of the fluctuational drag effect in the system. The results can be
easily generalized for other realizations of electron-hole bilayer.
