Testing Gravity with Cross-Correlation of Cosmic Microwave Background and Large-Scale-Structures of the Universe

In this thesis, we aim to compute the cross-correlation of the Integrated Sachs-Wolfe (ISW) effect with galaxy number densities for different models of gravity. The ISW effect arises due to gravitational potentials evolveìing in time. Thus, exploring the ISW effect is a powerful way to test gravity models. However, the ISW effect is faint compared to the other Cosmic Microwave Background temperature anisotropies. Cross-correlation with tracers of the Large-Scale-Structures ensures the detection of the ISW effect, making it a viable tool. The galaxy number count adopted follows a Euclid-like number distribution and we adopted an Effective Field Theory (EFT) formalism when treating the Dark Energy/Modified Gravity. The EFT action allows for more straightforward analytical and numerical results since it encompasses any model but it still can be mapped to specific cases. We computed the cross-correlations for state-of-the-art models using CAMB and EFTCAMB. For each model, we computed the Signal-to-Noise ratio according to an Euclid-like description and explored the parameter space that affects cross-correlation amplitudes.