  The growing wealth of cosmological observations places increasingly more
stringent constraints on dark energy and alternative gravity models.
Particularly successful in efficiently probing the vast model space has been
the effective field theory of dark energy and modified gravity, providing a
unified framework for generalised cosmological predictions. However, the
optimal parametrisation of the free time-dependent functions inherent to the
formalism is still unresolved. It should respect a multitude of requirements,
ranging from simplicity, generality, and representativity of known theories to
computational efficiency. But in particular, for theoretical soundness, the
parameter space should adhere to strict stability requirements. We have
recently proposed an inherently stable effective field theory with physical
basis of Planck mass evolution, sound speed of the scalar field fluctuation,
kinetic coefficient, and background expansion, which covers Horndeski models
with luminal speed of gravity. Here we devise a parametrisation of these 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 (sub)luminal scalar sound speed. The parametrisation
is simple yet general, conveniently represents a broad 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 linear
cosmological observations.
