Constraining Modified Gravity and Growth with Weak Lensing ⋆

The idea that we live in a Universe undergoing a period of acceleration is a new, yet strongly held, notion in cosmology. As this can, potentially, be explained with a modification to General Relativity we look at current cosmological data with the purpose of testing aspects of gravity. Firstly we constrain a phenomenological model (mDGP) motivated by a possible extra dimension. This is characterised by a parameter α which interpolates between α = 0 (LCDM) and α = 1 (the Dvali Gabadadze Porrati (DGP) model). In addition, we analyse general signatures of modified gravity given by the growth parameter γ and power spectrum parameter Σ. We utilise large angular scale (θ > 30 arcminutes) Weak Lensing data (CFHTLS-wide) in order to work in the more linear regime and then add, in combination, Baryon Acoustic Oscillations (BAOs) and Supernovae. We subsequently show that current weak lensing data is not yet capable of constraining either model in isolation. However we demonstrate that even at present this probe is highly beneficial, for in combination with BAOs and Supernovae we obtain α < 0.58 and α < 0.91 at 1σ and 2σ, respectively. Without the lensing data no constraint is possible. Inclusion of all angular scales (1 6 θ 6 230 arcminutes) allows a noticeable but not significant increase in the constraining power of the joint probes with α < 0.56 and α < 0.86 also at 1σ and 2σ, respectively. Both analyses correspond to a disfavouring of the flat DGP braneworld model (α = 1) at over 2σ. We highlight these are insensitive to potential systematics in the lensing data such as an underestimation of the shear at high redshift. For the growth signature γ we show that, in combination, these probes do not yet have sufficient constraining power. Finally, we look beyond these present capabilities and demonstrate that Euclid, a future weak lensing survey, will deeply probe the nature of gravity. A 1σ error of 0.104 is found for α (lmax = 500) whereas for the general modified signatures we forecast 1σ errors of 0.045 for γ and 0.25 for Σ0 (lmax = 500), which is further tightened to 0.038 for γ and 0.069 for Σ0 (lmax = 10000).