  Cosmology relies on a coarse-grained description of the universe, assumed to
be valid on large length scales. However, the nonlinearity of general
relativity makes coarse-graining extremely difficult. We here address this
problem by extending the Mori-Zwanzig projection operator formalism, a highly
successful coarse-graining method from statistical mechanics, towards general
relativity. Using the Buchert equations, we derive a new dynamic equation for
the Hubble parameter which captures the effects of averaging through a memory
function. This gives an empirical prediction for the cosmic jerk.
