  The structure of quantum vacuum in presence of gravity, and the corresponding
vacuum energy density $\rho_{v}$, is expected to depend on the coupling between
the UV scale $\ell_\mathrm{\textsf{UV}}$ and spacetime curvature. We determine
this coupling in an arbitrary freely falling frame characterised by it's
geodesic tangent $U^i(\tau)$. We show that local vacuum modes within a small
causal diamond based on $U^i(\tau)$, whose size is set by wavelength of the
modes, generically give a contribution $\rho_{0}$ to $\rho_v$ which, to leading
order, scales as: $\rho_{0} = \left( \pi \hbar c/2 \right) {\mathrm{\textsf R}}
\, {\ell_\mathrm{\textsf{UV}}}^{-2}$, where the curvature term $\mathrm{\textsf
R}=\alpha R_{ab} U^a U^b + \beta R$, and $(\alpha, \beta) \in \mathbb{R}$ are
constants. The genericness of this result arises from the fact that, although
the modes may reduce to Minkowski plane waves along $U^i(\tau)$, the
stress-energy tensor $T_{ab}$, since it depends on derivatives of the modes,
does not reduce to it's Minkowski value on $U^i(\tau)$. We discuss implications
of our result for vacuum processes in freely falling frames, particularly in
connection with certain aspects of the cosmological constant and horizon
entropy.
