  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
LCDM 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 Markov Chain Monte Carlo simulations to determine the
parameters of the model, using Type Ia Supernov\ae, 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 LCDM matter power
spectrum at both linear and non-linear scales and the LCDM and eDGP shear
signals are degenerate. This result does not hold with the HS prescription:
Euclid can distinguish the eDGP model from LCDM because their expected power
spectra roughly differ by the 3sigma uncertainty in the angular scale range
700<l<3000; on the contrary, the two models differ at most by the 1sigma
uncertainty over the range 500<l<3000 in the DES experiment and they are
virtually indistinguishable.
