[en] Hypothetical particles such as the heavy neutrino, the photino, or the sneutrino/emdash/generically called cosmions/emdash/may solve the so called missing mass problem. If they exist, the cosmions may close the Universe. In addition to their gravitational effect on cosmological scales, the cosmions may also be captured by stars and concentrate in their cores. Since cosmions are able to transport heat outside stellar cores much more efficiently than photons, they may seriously affect the thermodynamics of the inner layer of stars. We have done an exact calculation of the accretion rate of cosmions by main sequence stars and we have studied the suppression of their central convection. We concluded that central convection inside stars between 0.3 Msub solar and 1 Msub solar is broken in the presence of cosmions. 6 refs., 2 figs