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). We argue that although f(R) models are well described by the general [mu(a, k), eta(a, k)] parameterization, specific functional forms of mu, eta in the literature do not accurately represent f(R) behaviour, specifically at low redshift. 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 scalaron's 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 x 10(-30) eV at the similar to 20% level. However, the decay rate of the scalaron mass, with fiducial value nu = 1.5, can be constrained to similar to 3% uncertainty.