  The coherent production of vector mesons in photon-hadron interactions is
considered one of the most promising observables to probe the QCD dynamics at
high energies and the transverse spatial distribution of the gluons in the
hadron wave function. In this letter, we perform an exploratory study about the
dependence of the transverse momentum distributions, $d\sigma/dt$, on the model
assumed for the proton density profile. We consider a set of non-Gaussian
profiles and include them in the forward dipole-proton scattering amplitude
associated with the IP-sat model. We demonstrate that the predictions for
$d\sigma/dt$ are similar in the HERA kinematical range, but are very distinct
for values of $t$ that will be probed in future colliders. In particular, the
presence of diffractive dips in the $t$-distributions associated with the
production of $J/\Psi$ and $\rho$ mesons is strongly dependent on the model
assumed for the density profile. Similar conclusions are also derived when the
non-linear effects on the dipole-target interaction are disregarded. Our
results indicate that a future study of the coherent vector meson production at
large $t$ will be useful to constrain the spatial distribution of gluons within
the proton.
