Cluster abundances are oddly insensitive to canonical early dark energy. Early dark energy with sound speed equal to the speed of light cannot be distinguished from a quintessence model with the equivalent expansion history for $z<2$ but negligible e
arly dark energy density, despite the different early growth rate. However, cold early dark energy, with a sound speed much smaller than the speed of light, can give a detectable signature. Combining cluster abundances with cosmic microwave background power spectra can determine the early dark energy fraction to 0.3 % and distinguish a true sound speed of 0.1 from 1 at 99 % confidence. We project constraints on early dark energy from the Euclid cluster survey, as well as the Dark Energy Survey, using both current and projected Planck CMB data, and assess the impact of cluster mass systematics. We also quantify the importance of dark energy perturbations, and the role of sound speed during a crossing of $w=-1$.
Galileon gravity is a robust theoretical alternative to general relativity with a cosmological constant for explaining cosmic acceleration, with interesting properties such as having second order field equations and a shift symmetry. While either its
predictions for the cosmic expansion or growth histories can approach standard Lambda CDM, we demonstrate the incompatibility of both doing so simultaneously. Already current observational constraints can severely disfavor an entire class of Galileon gravity models that do not couple directly to matter, ruling them out as an alternative to Lambda CDM.
Galileon gravity offers a robust gravitational theory for explaining cosmic acceleration, having a rich phenomenology of testable behaviors. We explore three classes of Galileon models -- standard uncoupled, and linearly or derivatively coupled to ma
tter -- investigating the expansion history with particular attention to early time and late time attractors, as well as the linear perturbations. From the relativistic and nonrelativistic Poisson equations we calculate the generalizations of the gravitational strength (Newtons constant), deriving its early and late time behavior. By scanning through the parameters we derive distributions of the gravitational strength at various epochs and trace the paths of gravity in its evolution. Using ghost-free and stability criteria we restrict the allowed parameter space, finding in particular that the linear and derivative coupled models are severely constrained by classical instabilities in the early universe.
We examine general physical parameterisations for viable gravitational models in the $f(R)$ framework. This is related to the mass of an additional scalar field, called the scalaron, that is introduced by the theories. Using a simple parameterisation
for the scalaron mass $M(a)$ we show there is an exact correspondence between the model and popular parameterisations of the modified Poisson equation $mu(a,k)$ and the ratio of the Newtonian potentials $eta(a,k)$. However, by comparing the aforementioned model against other viable scalaron theories we highlight that the common form of $mu(a,k)$ and $eta(a,k)$ in the literature does not accurately represent $f(R)$ behaviour. We subsequently construct an improved description for the scalaron mass (and therefore $mu(a,k)$ and $eta(a,k)$) which captures their essential features and has benefits derived from a more physical origin. We study the scalarons observational signatures and show the modification to the background Friedmann equation and CMB power spectrum to be small. We also investigate its effects in the linear and non linear matter power spectrum--where the signatures are evident--thus giving particular importance to weak lensing as a probe of these models. Using this new form, we demonstrate how the next generation Euclid survey will constrain these theories and its complementarity to current solar system tests. In the most optimistic case Euclid, together with a Planck prior, can constrain a fiducial scalaron mass $M_{0} = 9.4 times 10^{-30}{rm eV}$ at the $sim 20 %$ level. However, the decay rate of the scalaron mass, with fiducial value $ u = 1.5$, can be constrained to $sim 3%$ uncertainty.
