Testing a phenomenologically extended DGP model with upcoming weak lensing surveys

A phenomenological extension of the well-known brane-world cosmology of Dvali, Gabadadze and Porrati (eDGP) has recently been proposed. In this model, a cosmological-constant-like term is explicitly present as a non-vanishing tension sigma on the brane, and an extra parameter alpha tunes the cross-over scale r(c), the scale at which higher dimensional gravity effects become non negligible. Since the Hubble parameter in this cosmology reproduces the same Lambda CDM expansion history, we study how upcoming weak lensing surveys, such as Euclid and DES (Dark Energy Survey), can confirm or rule out this class of models. We perform Monte CarloMarkov Chain simulations to determine the parameters of the model, using Type Ia Supernov, H(z) data, Gamma Ray Bursts and Baryon Acoustic Oscillations. We also fit the power spectrum of the temperature anisotropies of the Cosmic Microwave Background to obtain the correct normalisation for the density perturbation power spectrum. Then, we compute the matter and the cosmic shear power spectra, both in the linear and non-linear regimes. The latter is calculated with the two different approaches of Hu and Sawicki (2007) (HS) and Khoury and Wyman (2009) (KW). With the eDGP parameters coming from the Markov Chains, KW reproduces the Lambda CDM matter power spectrum at both linear and nonlinear scales and the Lambda CDM and eDGP shear signals are degenerate. This result does not hold with the HS prescription. Indeed, Euclid can distinguish the eDGP model from Lambda CDM because their expected power spectra roughly differ by the 3 sigma uncertainty in the angular scale range 700 less than or similar to l less than or similar to 3000; on the contrary, the two models differ at most by the 1 sigma uncertainty over the range 500 less than or similar to l less than or similar to 3000 in the DES experiment and they are virtually indistinguishable.