Positivity bounds on reconstructed Horndeski models

Positivity bounds provide conditions that a consistent UV-completion exists for a quantum field theory. We examine their application to Horndeski gravity models reconstructed from the effective field theory (EFT) of dark energy. This enables us to assess whether particular phenomenological parameterizations of the EFT functions reconstruct theories that respect or violate the positivity bounds. We find that commonly adopted EFT parametrizations, cast in terms of the dark energy density or power laws of the scale factor, only satisfy the positivity bounds in non-trivial regions of the parameter space. We then examine parameterizations of the inherently stable EFT basis, constructed to avoid gradient and ghost instabilities by default. In stark contrast, in this basis the positivity bounds either only provide constraints in a-priori unrealistic regions of the parameter space or do not provide any constraints on parameter values at all. The application of positivity bounds to common parametrizations of the standard EFT functions can therefore lead to artificial conclusions that the region of viable Horndeski modifications of gravity is highly constrained. Our results provide a strong motivation, in addition to the default avoidance of theoretical instabilities, for instead adopting parametrizations of the inherently stable EFT basis when testing dark energy and modified gravity models with forthcoming cosmological survey data.