Generalized Fluid Description

Abstract

So far in this thesis we have developed and constructed a formalism which allows the perturbed dark energy momentum tensor to be obtained for particular field contents of the dark sector. All modifications to the equations governing perturbations are contained within \({ {\delta }_{\scriptscriptstyle \mathrm{{E}}}}{U^{\mu }}_{\nu }\) and the perturbed fluid equations. In this chapter we rewrite some of these results to obtain what we call equations of state for dark sector perturbations. As the name suggests, these equations of state for perturbations play an identical role to the background equation of state \(P = w\rho \) used to close the background fluid equation \(\dot{\rho } = - 3\mathcal{H }(\rho +P)\). The structure of these equations of state for dark sector perturbations will be our window into detecting and discriminating between modified gravity theories.