The tale of two projects: covariance matrices and interaction in the dark sector

Covariance matrices are important tools for obtaining accurate constraints on cosmological parameters and, as such, it is essential to be able to identify their most relevant elements. The first part of my talk will be focused on our efforts to single out the most important modes of the DESY1 covariance matrix for cosmic shear, and also how we can use them as a means of comparison between covariance matrices produced by different codes. In the second part of my talk, I will start with an overview of two cosmological models with interaction in the dark sector. I will then move on to explain our work to constrain the parameters of these models using background observables, such as Type IA Supernovae, Baryon Acoustic Oscillation, Cosmological Clocks and the acoustic angular scale of the CMB. I will conclude by showing our results and findings when we took the Bayesian evidence to compare these models to the standard one.