Abstract The standard Λ Cold Dark Matter cosmological model provides an amazing
description of a wide range of astrophysical and astronomical data. However, there are a
few big open questions, that make the standard model look like a first-order approximation to
a more realistic scenario that still needs to be fully understood. In this Letter of Interest we
will list a few important goals that need to be addressed in the next decade, also taking into
account the current discordances present between the different cosmological probes, as the�…