  We study the effect of the Chern-Simons gauge fields on the possible
transition from two decoupled composite fermion metals to the interlayer
coherent composite fermion state proposed by Alicea et al. [Phys. Rev. Lett.
103, 256403 (2009)] in a symmetrically doped quantum Hall bilayer with total
Landau level filling fraction $\nu_{tot} = 1$. In this transition, interlayer
Coulomb repulsion leads to excitonic condensation of composite fermions which
are then free to tunnel coherently between layers. We find that this coherent
tunneling is strongly suppressed by the layer-dependent Aharonov-Bohm phases
experienced by composite fermions as they propagate through the fluctuating
gauge fields in the system. This suppression is analyzed by treating these
gauge fluctuations within the random-phase approximation and calculating their
contribution to the energy cost for forming an exciton condensate of composite
fermions. This energy cost leads to (1) an increase in the critical interlayer
repulsion needed to drive the transition; and (2) a discontinuous jump in the
energy gaps to out-of-phase excitations (i.e., excitations involving currents
with opposite signs in the two layers) at the transition.
