Constraining dark sector perturbations II: ISW and CMB lensing tomography

Any Dark Energy (DE) or Modified Gravity (MG) model that deviates from a cosmological constant requires a consistent treatment of its perturbations, which can be described in terms of an effective entropy perturbation and an anisotropic stress. We have considered a recently proposed generic parameterisation of DE/MG perturbations and compared it to data from the Planck satellite and six galaxy catalogues, including temperature-galaxy (Tg), CMB lensing-galaxy and galaxy-galaxy (gg) correlations. Combining these observables of structure formation with tests of the background expansion allows us to investigate the properties of DE/MG both at the background and the perturbative level. Our constraints on DE/MG are mostly in agreement with the cosmological constant paradigm, while we also find that the constraint on the equation of state w (assumed to be constant) depends on the model assumed for the perturbation evolution. We obtain $w=-0.92^{+0.20}_{-0.16}$ (95% CL; CMB+gg+Tg) in the entropy perturbation scenario; in the anisotropic stress case the result is $w=-0.86^{+0.17}_{-0.16}$. Including the lensing correlations shifts the results towards higher values of w. If we include a prior on the expansion history from recent Baryon Acoustic Oscillations (BAO) measurements, we find that the constraints tighten closely around $w=-1$, making it impossible to measure any DE/MG perturbation evolution parameters. If, however, upcoming observations from surveys like DES, Euclid or LSST show indications for a deviation from a cosmological constant, our formalism will be a useful tool towards model selection in the dark sector.

Cluster Probes of Dark Energy Clustering

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 early 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 $w=-1$.

Modified Gravity: the CMB, Weak Lensing and General Parameterisations

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.

Complementarity of Future Dark Energy Probes

In recent years a plethora of future surveys have been suggested to constrain the nature of dark energy. In this paper we adapt a binning approach to the equation of state factor ``w and discuss how future weak lensing, galaxy cluster counts, Supernovae and baryon acoustic oscillation surveys constrain the equation of state at different redshifts. We analyse a few representative future surveys, namely DES, PS1, WFMOS, PS4, EUCLID, SNAP and SKA, and perform a principal component analysis for the ``w bins. We also employ a prior from Planck cosmic microwave background measurements on the remaining cosmological parameters. We study at which redshifts a particular survey constrains the equation of state best and how many principal components are significantly determined. We then point out which surveys would be sufficiently complementary. We find that weak lensing surveys, like EUCLID, would constrain the equation of state best and would be able to constrain of the order of three significant modes. Baryon acoustic oscillation surveys on the other hand provide a unique opportunity to probe the equation of state at relatively high redshifts.