Abstract
We present a methodology for computing model independent perturbations in dark energy and modified gravity. This is done from the Lagrangian for perturbations, by showing how field content, symmetries, and physical principles are often sufficient ingredients for closing the set of perturbed fluid equations. The fluid equations close once ``equations of state for perturbations'' are identified: these are linear combinations of fluid and metric perturbations which construct gauge invariant entropy and anisotropic stress perturbations for broad classes of theories. Our main results are the proof of the equation of state for perturbations presented in a previous paper, and the development of the required calculational tools.
Highlights
The important point is that we obtain consistent cosmological perturbations from a model independent formalism: we are able to remain agnostic about the functional form of the Lagrangian
Our approach is similar since we identify all the PPF functions for modified gravity theories satisfying various restrictions
We have shown that the Kinetic Gravity Braiding (KGB) theory has an activation matrix which is of precisely the same form as that we derived from a model independent approach in (4.3)
Summary
Rather than follow the usual route and cast the parameterization in terms of “fields”, we use the more physically intuitive “fluid” description. Only certain derivatives and combinations of fields in the underlying dark sector theory will go into modifying the sources of given components of the perturbed gravitational field equations. This approach is already commonly used at the level of the cosmological background. It should be clear that all that needs to be specified is the entropy perturbation wΓ and the anisotropic stress Πμν of the dark fluid: these are the two “physical” pieces of freedom which a dark sector theory will end up specifying Once these are provided in terms of variables whose equations of motion are already specified, the system of equations closes and can be solved. The most pertinent question our approach is able to answer is precisely which of these dynamical components are required to construct the gauge invariant entropy perturbation and the anisotropic stress to describe broad classes of modified gravity and dark energy theories
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