  The field theoretic renormalization group (RG) is applied to the model of a
near-equilibrium fluid coupled to a scalar field (like temperature or density
of an impurity) which is active, that is, influencing the dynamics of the fluid
itself. It is shown that the only possible nontrivial infrared (IR) asymptotic
regimes are governed by "passive" fixed points of the RG equations, where the
back reaction is irrelevant. This result reminds of that obtained in [Nandy and
Bhattacharjee, J. Phys. A: Math. Gen. {\bf 31}, 2621 (1998)] in a model
describing active convection by fully developed turbulence. Furthermore, we
establish the existence of "exotic" fixed points with negative and complex
effective couplings and transport coefficients that may suggest possible
directions for future studies.
