  We present a (hopefully) novel calculation of the vacuum energy in expanding
FLRW spacetimes based on the renormalization of quantum field theory in
non-zero backgrounds. We compute the renormalized effective action up to the
$2-$point function and then apply the formalism to the cosmological backgrounds
of interest. As an example we calculate for quasi de Sitter spacetimes the
leading correction to the vacuum energy given by the tadpole diagram and show
that it behaves as $\sim H_0^2 \Lambda_{\rm pl}$ where $H_0$ is the Hubble
constant and $\Lambda_{\rm pl}$ is the Planck constant. This is of the same
order of magnitude as the observed dark energy density in the universe.
