Cosmological tests of fundamental physics

The standard model of Cosmology, or the $\Lambda$CDM model, is able to describe remarkably well a plethora of observations with only six parameters. Nonetheless, several questions about its very nature have yet to be answered. Chief amongst them is the nature of Dark Energy, responsible for the observed acceleration of the Universe. While in the $\Lambda$CDM model Dark Energy is modelled via the cosmological constant $\Lambda$, its observed value cannot be reconciled with the predictions of quantum field theory, the framework at the basis of the standard model of particle physics. Modifications of General Relativity, known as modified gravity, offer an alternative approach to Dark Energy. The growth of large scale structure is modified in alternative gravity theories in ways that can be tested using cosmological data. We present a comprehensive analysis of a set of scalar-tensor theories of gravity that exhibit the chameleon screening mechanism. This mechanism hides the force mediated by the extra scalar from detection in local and solar system tests of gravity, while still leaving imprints in the cosmological observables. With the increasing precision of cosmological surveys, finer effects must be included in the theoretical predictions. This is the case for the total mass of neutrinos that affect the structure formation at the percent level in a way that could be degenerate with modified gravity. Being able to break this degeneracy requires ability to account for the mass of neutrinos while constraining modified gravity theories. We thus introduce a consistent treatment of massive neutrinos in the phenomenological $\mu-\gamma$ framework and update the popular code MGCAMB used to constrain modified gravity models. We have also introduced the option for MGCAMB to work with general background histories where Dark Energy evolves with time. It has been recently shown that a dynamical Dark Energy with density that increases with time is able to alleviate the tensions between different datasets within the $\Lambda$CDM model. Modified gravity theories provide a framework to explain such behaviour of Dark Energy and we perform a reconstruction of the Lagrangian of Generalized Brans-Dicke theories from the observed expansion history of the Universe. We then study the viability of the such theories and ways of testing them with future data. Another challenge for upcoming CMB experiments is the detection of the primordial gravitational wave background in the B-mode polarization signal. Such a background is predicted by Inflation, a period of exponential expansion in the early Universe, which is the paradigm behind the choice of the initial conditions in the $\Lambda$CDM model. CMB B-modes also offer a powerful way to test the existence of primordial magnetic fields in the early Universe. These can also arise from the inflationary mechanism or be generated during phase transitions in the early universe. We have developed a publicly available code, dubbed MagCAMB, that computes the CMB anisotropies generated by primordial magnetic fields. We also derived the tightest constrain to date on the primordial magnetic field amplitude using the CMB spectra from the Planck satellite and the B-mode measurements by the South Pole Telescope.