Testing and Emulating Modified Gravity on Cosmological Scales
  This thesis introduces a set of methods for testing models of modified
gravity using galaxy clusters. In particular, a technique for constraining
models with a chameleon screening is introduced. In addition, the outlined
technique is expanded to test a wider class of models, such as the theory of
emergent gravity. Finally, the first part of the thesis is concluded by
adapting the mentioned tests for model independent constraints. The obtained
results indicate that galaxy clusters can be used to obtain some of the most
powerful constraints on cosmological scales.
  The second part of the thesis is dedicated to the topic of cosmological
emulators. More specifically, a technique of emulating cosmological N-body
simulation output data based on machine learning is introduced. Generative
adversarial networks (GANs) are used to emulate dark matter-only as well as
hydrodynamical simulation data. In addition, N-body modified gravity
simulations are explored as well. The presented investigation of the GAN
algorithm shows that such emulators offer a powerful, fast and efficient way of
producing simulation output data with different cosmological parameters. The
power spectrum analysis indicates a 1-20% difference between the training and
the generated data depending on the dataset used and whether Gaussian smoothing
is applied or not.
