  We develop a worldline approach to quantum gravity in D=4. Using the
background field method we consider the covariantly gauge fixed
Einstein-Hilbert action with cosmological constant, and find a worldline
representation of the differential operators identified by its quadratic
approximation. We test it by computing the correct one-loop divergencies.
Alternative worldline methods, such as the use of the O(4) spinning particle
that is known to describe correctly the propagation of a massless spin 2
particle in D=4, find obstructions in the coupling to an arbitrary background
metric, apparently preventing a more extensive use in perturbative descriptions
of quantum gravity. We expect that our model might simplify calculations of
one-loop amplitudes with respect to standard quantum field theoretical methods.
