Cosmological constraints from the CFHTLenS shear measurements using a new, accurate and flexible way of predicting nonlinear mass clustering

We explore the cosmological constraints from cosmic shear using a new way of modelling the non-linear matter correlation functions. The new formalism extends the method of Angulo & White (2010), which manipulates outputs of $N$-body simulations to represent the three-dimensional nonlinear mass distribution in different cosmological scenarios. We show that predictions from our approach for shear two-point correlations at $1$ to $300$ arcmin separations are accurate at the $\sim 10$% level, even for extreme changes in cosmology. For moderate changes, with target cosmologies similar to that preferred by analyses of recent Planck data, the accuracy is close to $\sim 5$%. We combine this approach with a MonteCarlo Markov Chain sampler to explore constraints on a $\mathrm{\Lambda }$CDM model from the shear correlation functions measured in the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS). We obtain constraints on the parameter combination $\sigma_8 (\Omega_m/0.27)^{0.6} = 0.801 \pm 0.028$. Combined with results from CMB data, we obtain marginalised constraints on ${\sigma }_8=0.81\pm 0.01$ and $\Omega_m = 0.29 \pm 0.01$. These results are fully compatible with previous analyses, which supports the validity of our approach. We discuss the advantages of our method and the potential it offers, including a path to incorporate in detail the effects of baryons, among others effects, in future high-precision cosmological analyses.