  We have developed a proper path integral formalism consistent with the
deformed version of the quantum mechanics which contains a maximum observable
length scale at the order of the Cosmological particle horizon, existing in
cosmology. First, we have presented the modifications to the classical
mechanics which shows non-minimal effects on the equation of motion of a
particle. Next, we have provided representation of the deformed quantum
mechanical algebra. With this algebra in hand, we have calculated the general
form of the path integral propagator in this deformed background. Finally, as a
most simple case, we have built up the explicit form of the free particle
propagator. The modifications to the free particle propagator shows some
non-trivial effects in this case, which can have some important significance.
