Cosmological Constraints on an Invisibly Decaying Higgs Boson

Working in the context of a proposal for collisional dark matter, we derive bounds on the Higgs boson coupling $g^{\prime}$ to a stable light scalar particle, which we refer to as phion ($\phi$), required to solve problems with small scale structure formation which arise in collisionless dark matter models. We discuss the behaviour of the phion in the early universe for different ranges of its mass. We find that a phion in the mass range of 100 MeV is excluded and that a phion in the mass range of 1 GeV requires a large coupling constant, $g^{\prime} \gsim 2$, and $m_h \lsim 130$ GeV in order to avoid overabundance, in which case the invisible decay mode of the Higgs boson would be dominant.