  Scalars are widely used in cosmology to model novel phenomena such as the
late-time cosmic acceleration. These are effective field theories with highly
nonlinear interactions, including Horndeski theory/generalized galileon and
beyond. We use the latest fully crossing symmetric positivity bounds to
constrain these cosmological EFTs. These positivity bounds, based on
fundamental principles of quantum field theory such as causality and unitarity,
are able to constrain the EFT coefficients both from above and below. We first
map the mass dependence of the fully crossing symmetric bounds, and find that a
nonzero mass generically enlarges the positivity regions. We show that
fine-tunings in the EFT construction can significantly reduce the viable
regions and sometimes can be precarious. Then, we apply the positivity bounds
to several models in the Horndeski class and beyond, explicitly listing the
ready-to-use bounds with the model parameters, and discuss the implications for
these models. The new positivity bounds are found to severely constrain some of
these models, in which positivity requires the mass to be parametrically close
to the cutoff of the EFT, effectively ruling them out. The examples include
massive galileon, the original beyond Horndeski model, and DHOST theory with
unity speed of gravity and nearly constant Newton's coupling.
