  We discuss the fluctuation-induced force, a finite-temperature analog of the
Casimir force, between two inclusions embedded in a fluid membrane under
tension. We suggest a method to calculate this Casimir interaction in the most
general case, where membrane fluctuations are governed by the combined action
of surface tension, bending modulus, and the Gaussian rigidity. We find that
the surface tension strongly modifies the power law in the separation
dependence of the Casimir interaction. This results in a strong suppression of
the Casimir force at separations beyond a characteristic length, which could
affect protein aggregation dynamics in cell membranes.
