Abstract
We present current and future constraints on equations of state for dark sector perturbations. The equations of state considered are those corresponding to a generalized scalar field model and time-diffeomorphism invariant ℒ(g) theories that are equivalent to models of a relativistic elastic medium and also Lorentz violating massive gravity. We develop a theoretical understanding of the observable impact of these models. In order to constrain these models we use CMB temperature data from Planck, BAO measurements, CMB lensing data from Planck and the South Pole Telescope, and weak galaxy lensing data from CFHTLenS. We find non-trivial exclusions on the range of parameters, although the data remains compatible with w=−1. We gauge how future experiments will help to constrain the parameters. This is done via a likelihood analysis for CMB experiments such as CoRE and PRISM, and tomographic galaxy weak lensing surveys, focussing in on the potential discriminatory power of Euclid on mildly non-linear scales.
Highlights
This leaves a residual vector degree of freedom and a massive graviton. We call this class of theories the time diffeomorphism invariant (TDI) L(g) theories. These TDI L(g) theories have been studied in the literature, under the name of elastic dark energy [46,47,48]; the theory is equivalent to a particular brand of Lorentz violating massive gravities [37]
We have performed a similar analysis when varying the α parameter in the generalized scalar field (GSF) models: for 0 ≤ α ≤ 1 we find no qualitative difference in the lensing potential from that we presented in figure 4(a) — there certainly aren’t any features which pop up on small and large scales as there are in the TDI L(g) models
In figure we show the constraints on c2s in the TDI L(g) models and in figure the constraints on α, β1, β2 in the GSF models
Summary
The equations of state for perturbations formalism was designed to allow meaningful and model independent statements about the allowed properties of the dark sector to be extracted from observations. In (2.3), Γ and ΠS are the gauge invariant entropy and anisotropic stress perturbations respectively and this property means that it is sensible to use these functions to specify the modified gravity/dark energy theory. The main idea behind our approach is to specify two ingredients: (i) the field content of the dark sector, and (ii) ask for a particular set of symmetries or principles to be respected and not to specify the actual Lagrangian After these two ingredients are laid down, we are able to obtain all the freedom at the level of linearized perturbations, since these two ingredients are sufficient information for obtaining a precise form of the coefficients {Ai, Bi} in the equations of state for perturbations (with prescribed scale dependence), and there will be nothing else left to specify to characterize the perturbations. This generalization is not of practical interest, at least for the foreseeable future
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