  We derive bounds on the Higgs boson coupling $g^{\prime}$ to a stable light
scalar which is regarded as a collisional dark matter candidate. We study the
behaviour of this scalar, that we refer to as phion ($\phi$), in the early
Universe for different ranges of its mass. We find that a phion in the mass
range of $100 \mev$ is excluded, while if its mass is about $1 \gev$, a rather
large coupling constant, $g^{\prime} \gsim 2$, and $m_h \lsim 130 \gev$ are
required in order to avoid overabundance. In the latter case, the invisible
decay mode of the Higgs boson is dominant.
