  Following our previous work wherein the leading order effective action was
computed in the covariant effective field theory of gravity, here we specialize
the effective action to the FRW spacetime and obtain the effective Friedmann
equations. In particular, we focus our attention on studying the cosmological
implications of the non-local terms when each of them is combined with the
Einstein-Hilbert action. We obtain both analytical and iterative solutions to
the effective background equations in all the cases and also briefly comment on
the consistency between the iterative and numerical solutions whenever
possible. We find that among all the non-local terms, the imprints induced by
$R\frac{1}{\square^2}R$ are very significant. Interpreting these corrections as
an effective dark energy component characterized by an equation of state
parameter, we find that the $R\frac{1}{\square^2}R$ correction can indeed lead
to an accelerated expansion of the universe at the present epoch even in the
absence of a cosmological constant. We briefly discuss some phenomenological
consequences of our results.
