Illuminating the Dark Sector: Searching for new interactions between dark matter and dark energy

The current standard model of cosmology - the ΛCDM model - is appropriately named after its controversial foreign ingredients: a cosmological constant (Λ) that accounts for the recent accelerated expansion of the Universe and cold dark matter needed to explain the formation and dynamics of large scale structures. Together, these form the dark sector, whose nature remains a mystery. After 25 years of withstanding confirmation and support for the ΛCDM model, enough to bypass some of its unclear theoretical issues, this paradigm is facing its biggest crisis yet. The rapid advent of technology has brought cosmology to an unprecedented observational era, with increased technical precision and the emergence of independent measures, including probes of phenomena that were thought impossible to detect or even exist, such as the gravitational ripples that propagate in the spacetime. However, such precision has unveiled cracks in the porcelain of ΛCDM, with pieces that seem glued together and difficult to reconcile. Particularly worrying is the apparent lack of compatibility between measurements of the Universe’s present expansion rate based on local measurements and those based on phenomena that occurred far in the early Universe and that can only be translated into present quantities through physical propagation under a cosmological model. In this dissertation, we delve into extensions to the standard model that consider alternatives to the mysterious nature of the dark sector and any possible new interactions therein. We analyse these alternative models, hoping to identify measurable observational signatures of extra degrees of freedom in the dark sector. For this purpose, we focus on Markov Chain Monte Carlo sampling techniques by exploiting recent observational data and their combination to constrain and assess the validity of the model’s parameter space. The extended frameworks investigated are only found to be marginally or not at all favoured over the ΛCDM model, ultimately falling short of resolving the tensions present in the latter. We conclude with a forecast on the constraining power of upcoming gravitational wave detectors as standard sirens, independently and combined with current background data. By generating simulated standard siren event catalogues following the specifications predicted by the proposed missions, we discuss how an emerging avenue for independent data may be decisive in constraining alternative theories of gravity and shed light on the nature of the dark sector.