  We calculate the Casimir energy of a massless scalar field in a cavity formed
by nearby parallel plates orbiting a rotating spherical body surrounded by
quintessence, investigating the influence of the gravitational field on that
energy, at zero temperature. This influence includes the effects due to the
spacetime dragging caused by the source rotation as well as those ones due to
the quintessence. We show that the energy depends on all the involved
parameters, as source mass, angular momentum and quintessence state parameter,
for any radial coordinate and polar angle. We show that at the north pole the
Casimir energy is not influenced by the quintessential matter. At the
equatorial plane, when the quintessence is canceled, the result obtained in the
literature is recovered. Finally, constraints in the quintessence parameters
are obtained from the uncertainty in the current measurements of Casimir
effect.
