  The diffractive photoproduction of rho mesons, e p \to e rho Y, with large
momentum transfer squared at the proton vertex, |t|, is studied with the H1
detector at HERA using an integrated luminosity of 20.1 pb^{-1}. The
photon-proton centre of mass energy spans the range 75 < W < 95 GeV, the photon
virtuality is restricted to Q^2 < 0.01 GeV^2 and the mass M_Y of the proton
remnant is below 5 GeV. The t dependence of the cross section is measured for
the range 1.5 < |t| < 10.0 GeV^2 and is well described by a power law, dsigma/
d|t| \propto |t|^{-n}. The spin density matrix elements, which provide
information on the helicity structure of the interaction, are extracted using
measurements of angular distributions of the rho decay products. The data
indicate a violation of s-channel helicity conservation, with contributions
from both single and double helicity-flip being observed. The results are
compared to the predictions of perturbative QCD models.
