1304.4840 (Jerome Gleyzes et al.)

Essential Building Blocks of Dark Energy    [PDF]

Jerome Gleyzes, David Langlois, Federico Piazza, Filippo Vernizzi

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 time-dependent coefficients of three of these operators being determined only by the background evolution. 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 show that Horndeski's-or generalized Galileon-theories can be described, up to linear order, by only six of the seven operators mentioned above. 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.

View original: http://arxiv.org/abs/1304.4840