Constraining Modified Gravity and Growth with Weak Lensing

The idea that we live in a Universe undergoing a period of acceleration is a 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 $\alpha$ which interpolates between (LCDM) and (the Dvali Gabadadze Porrati (DGP) model). In addition, we analyse general signatures of modified gravity given by the growth parameter $\gamma$ and power spectrum parameter $\Sigma$. We utilise Weak Lensing data (CFHTLS-wide) in combination with Baryon Acoustic Oscillations (BAOs) and Supernovae data. We show that current weak lensing data is not yet capable of constraining either model in isolation. However we demonstrate that this probe is highly beneficial, for in combination with BAOs and Supernovae we obtain $\alpha < 0.58$ and $\alpha < 0.91$ at $1\sigma$ and $2\sigma$, respectively. Without the lensing data no constraint is possible. Both analyses disfavour the flat DGP braneworld model ($\alpha = 1$) at over $2\sigma$. We highlight these are insensitive to potential systematics in the lensing data. For the growth signature $\gamma$ 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 $1\sigma$ error of 0.104 is found for $\alpha$ ($l_{max} = 500$) whereas for the general modified signatures we forecast $1\sigma$ errors of 0.045 for $\gamma$ and 0.25 for $\Sigma_{0}$ ($l_{max} = 500$), which is further tightened to 0.038 for $\gamma$ and 0.069 for $\Sigma_{0}$ ($l_{max} = 10000$).