  The spacetime evolution of massless spinning particles in a Robertson-Walker
background is derived using the deterministic system of equations of motion due
to Papapetrou, Souriau and Saturnini. A numerical integration of this system of
differential equations in the case of the standard model of cosmology is
performed. The deviation of the photon worldlines from the null geodesics is of
the order of the wavelength. Perturbative solutions are also worked out in a
more general case. An experimental measurement of this deviation would test the
acceleration of our expanding universe.
