Inherently stable effective field theory for dark energy and modified gravity

The growing wealth of cosmological observations places succeedingly more stringent constraints on dark energy and alternative gravity models. To most effectively exploit this data and infer the broadest of implications for the vast conceivable model space, the development of unified frameworks for generalised cosmological predictions has become an important endeavour. Particularly successful for this purpose has been the effective field theory of dark energy and modified gravity. In its practical application the formalism is however still restrained by questions surrounding the adequate parametrisation of the free time-dependent functions inherent to the framework, which should respect a multitude of requirements, ranging from simplicity, generality, and representativity of known theories to the computational efficiency. But in particular, for theoretical soundness, the parameter space should adhere to strict stability requirements. Focussing on Horndeski gravity with luminal speed of gravity, we explore the inherently stable effective field theory that we have recently introduced with the physical basis functions of Planck mass evolution, sound speed of the scalar field fluctuation, kinetic coefficient, and background expansion. We devise a parametrisation of the basis functions that can straightforwardly be configured to evade theoretical pathologies such as ghost or gradient instabilities or to accommodate further theoretical priors such as a luminal or subluminal scalar sound speed. The parametrisation is simple yet general, conveniently provides an accurate representation of a range of known dark energy and gravitational theories, and with a simple additional approximation can be rendered numerically highly efficient. Finally, by operating in our new basis, we show that there are no general limitations from stability requirements on the current values that can be assumed by the phenomenological modification of the Poisson equation and the gravitational slip besides the exclusion of anti-gravity. The inherently stable effective field theory is ready for implementation in parameter estimation analyses employing current or future cosmological observations amenable to linear perturbation theory.