  We compute the renormalised energy momentum tensor of a free scalar field
coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU),
RxS^n, with arbitrary low energy effective operators (up to mass dimension
n+1). A generic class of regulators is used, together with the Abel-Plana
formula, leading to a manifestly regulator independent result. The general
structure of the divergences is analysed to show that all the gravitational
couplings (not just the cosmological constant) are renormalised for an
arbitrary regulator. Various commonly used methods (damping function,
point-splitting, momentum cut-off and zeta function) are shown to, effectively,
belong to the given class. The final results depend strongly on the parity of
n. A detailed analytical and numerical analysis is performed for the behaviours
of the renormalised energy density and a quantity `sigma' which determines if
the strong energy condition holds for the `quantum fluid'. We briefly discuss
the quantum fluid back-reaction problem, via the higher dimensional Friedmann
and Raychaudhuri equations, observe that equilibrium radii exist and unveil the
possibility of a `Casimir stabilisation of Einstein Static Universes'.
