Essential Building Blocks of Dark Energy
  We propose a minimal description of single field dark energy/modified gravity
within the effective field theory formalism for cosmological perturbations,
which encompasses most existing models. We start from a generic Lagrangian
given as an arbitrary function of the lapse and of the extrinsic and intrinsic
curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as
time slicing the uniform scalar field hypersurfaces. Focusing on linear
perturbations, we identify seven Lagrangian operators that lead to equations of
motion containing at most two (space or time) derivatives, the background
evolution being determined by the time dependent coefficients of only three of
these operators. We then establish a dictionary that translates any existing or
future model whose Lagrangian can be written in the above form into our
parametrized framework. As an illustration, we study Horndeski's-or generalized
Galileon-theories and show that they can be described, up to linear 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
while remaining second order. Finally, in order to make the link with
observations, we provide the entire set of linear perturbation equations in
Newtonian gauge, the effective Newton constant in the quasi-static
approximation and the ratio of the two gravitational potentials, in terms of
the time-dependent coefficients of our Lagrangian.
