  In the Hamiltonian formulation of General Relativity the energy associated to
an asymptotically flat space-time with metric $g_{\mu\nu}$ is related to the
Hamiltonian $H_{GR}$ by $E=H_{GR}[g_{\mu\nu}]-H_{\rm GR}[\eta_{\mu\nu}]$, where
the subtraction of the flat-space contribution is necessary to get rid of an
otherwise divergent boundary term. This classic result indicates that the
energy associated to flat space does not gravitate. We apply the same principle
to study the effect of zero-point fluctuations of quantum fields in cosmology,
proposing that their contribution to the cosmic expansion is obtained computing
the vacuum energy of quantum fields in a FRW space-time with Hubble parameter
$H(t)$ and subtracting from it the flat-space contribution. [...] After
renormalization, this produces a renormalized vacuum energy density $\sim
M^2H^2(t)$, where $M$ is the scale where quantum gravity sets is, so for $M$ of
order of the Planck mass a vacuum energy density of the order of the critical
density can be obtained without any fine tuning. The counterterms can be chosen
so that the renormalized energy density and pressure satisfy $p=w\rho$, with
$w$ a parameter that can be fixed by comparison to the observed value, so in
particular one can chose $w=-1$. An energy density evolving in time as $H^2(t)$
is however observationally excluded as an explanation for the dominant dark
energy component which is responsible for the observed acceleration of the
universe. We rather propose that zero-point vacuum fluctuations provide a new
subdominant "dark" contribution to the cosmic expansion that, for a UV scale
$M$ slightly smaller than the Planck mass, is consistent with existing limits
and potentially detectable.
