Forthcoming wide field weak lensing surveys, such as DES and Euclid, present the possibility of using lensing as a tool for precision cosmology. This means exciting times are ahead for cosmological constraints for different gravity and dark energy models, but also presents possible new challenges in modelling, both non-standard physics and the lensing itself.
In this thesis I look at how well DES and Euclid will be able to discriminate between different cosmological models and utilise lensing’s combination of geometry and growth information to break degeneracies between models that fit geometrical probes, but may fail to fit the observed growth. I have focussed mainly on the non-linear structure growth regime, as these scales present the greatest lensing signal, and therefore greatest discriminatory power.
I present the predicted discriminatory power for modified gravities models, DGP and f(R), including non-linear scales for DES and Euclid. Using the requirement that modified gravities must tend to general relativity on small scales, we use the fitting formula proposed by Hu & Sawicki to calculate the non-linear power spectrum for our lensing predictions. I demonstrate the improved discriminatory power of weak lensing for these models when non-linear scales are included, and show that not allowing for the GR asymptote at small scales can lead to an overestimation in the strength of the constraints. I then parameterise the non-linear power spectrum to include the growth factor, and demonstrate that even including these extra parameters there is still more power in a full non-linear analysis than just using linear scales.
I then present non-linear weak lensing predictions for coupled dark energy models using the CoDECS simulations. I obtain predictions for the discriminatory power of DES and Euclid in distinguishing between ΛCDM and coupled dark energy models; I show that using the non-linear lensing signal we could discriminate between ΛCDM and exponential constant coupling models with β0 ≥ 0.1 at 99.994% confidence level with a DES-like survey, and β0 ≥ 0.05 at 99.99994% confidence level with Euclid. I also demonstrate that estimating the coupled dark energy models’ non-linear power spectrum, using the ΛCDM Halofit fitting formula, results in biases in the shear correlation function that exceed the survey errors.
I then present weak lensing predictions for DES and Euclid, and the CMB temperature power spectrum expected for Planck for fast transition adiabatic unified dark matter models. I demonstrate that in order to constrain the parameters in this model a high and low redshift observational probe is required. I show that for a ΛCDM fiducial, Planck could constrain zt > 5 at a 95% confidence level, and DES and Euclid could constrain the maximum time the transition can take to < 5 × 10−6/H0 at a 95% confidence level.
Finally I look at a full general relativistic model of lensing. I adopt the use of a Lemaitre-Tolman-Bondi model, with and without pressure, to model an over density in an expanding background in a continuous space time. I use this to examine how the modelling of intermediate scales affects lensing quantities, and whether, as has been suggested recently, the cosmological constant has a direct effect on the lensing observables.