Cosmological Bounds on an Invisibly Decaying Higgs Boson

We derive bounds on the Higgs boson coupling $g^{\mathrm{\prime }}$ 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 ($\varphi$), in the early Universe for different ranges of its mass. We find that a phion in the mass range of $100\text{mev}$ is excluded, while if its mass is about $1\text{gev}$, a rather large coupling constant, $g^{\mathrm{\prime }}\text{gsim}2$, and $m_h\text{lsim}130\text{gev}$ are required in order to avoid overabundance. In the latter case, the invisible decay mode of the Higgs boson is dominant.