  LHC experiments can provide a remarkable sensitivity to exotic metastable
massive particles, decaying with significant displacement from the interaction
point. The best sensitivity is achieved to models where the production and
decay occur due to different coupling constants, and the lifetime of exotic
particles determines the probability of decay within a detector. The lifetimes
of such particles can be independently limited from standard cosmology, in
particular the Big Bang Nucleosynthesis. In this paper, we analyze the
constraints on the simplest scalar model coupled through the Higgs portal,
where the production occurs via $h\to SS$, and the decay is induced by the
small mixing angle of the Higgs field $h$ and scalar $S$. We find that
throughout the most part of the parameter space, $2 m_\mu < m_S < m_h/2$, the
lifetimes of exotic particle has to be less than 0.1 seconds, while below
$2m_\mu$ it could grow to about a second. The strong constraints on lifetimes
are induced by the nucleonic and mesonic decays of scalars that tend to raise
the $n/p$ ratio. Strong constraints on lifetimes of the minimal singlet
extensions of the Higgs potential is a welcome news for the MATHUSLA proposal
that seeks to detect displaced decays of exotic particles produced in the LHC
collisions. We also point out how more complicated exotic sectors could evade
the BBN lifetime constraints.
