Triple crossing positivity bounds, mass dependence and cosmological scalars: Horndeski theory and DHOST

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. Also, massive galileon's positivity region appears to be in tension with observational constraints, while a $(\partial\phi)^4$ modified model is more accommodating phenomenologically.