  Requiring the existence of a unitary, causal and local UV-completion places a
set of positivity bounds on the corresponding effective field theories (EFTs).
We discuss the obstructions and possibility in applying the positivity bound to
cosmology, in particular the EFT of cosmological perturbations. Taking a
$c_T=1$ beyond-Horndeski EFT as an illustrative example, we derive such bounds,
which incorporate the cosmological correction of order $H^2/\Lambda^2$,
$\Lambda$ being the cutoff scale. The derived bounds are applied to slow-roll
inflation with beyond Horndeski operators. It is found that the cosmological
positivity bounds may be either stronger or weaker than their flat space
counterpart.
