Essential building blocks of dark energy

International audienceWe propose a minimal description of single field dark energy/modified gravitywithin the effective field theory formalism for cosmologicalperturbations, which encompassesmost existing models. We start from a generic Lagrangian given as an arbitrary function ofthe lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces inunitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusingon linear perturbations, we identify seven Lagrangian operators that lead to equations ofmotion containing at most two (space or time) derivatives, the background evolution beingdetermined by the time-dependent coefficients of only three of these operators. We thenestablish a dictionary that translates any existing or future model whose Lagrangian can bewritten in the above form into our parametrized framework. As an illustration, we studyHorndeski’s — or generalized Galileon — theories and show that they can be described, up tolinear order, by only six of the seven operators mentioned above. This implies, remarkably,that the dynamics of linear perturbations can be more general than that of Horndeski whileremaining second order. Finally, in order to make the link with observations, we provide theentire set of linear perturbation equations in Newtonian gauge, the effective Newton constantin the quasi-static approximation and the ratio of the two gravitational potentials,in terms of the time dependent coefficients of our Langrangia