Abstract
The standard $Łambda$ 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 Hubble constant $H_0$ value, the $\sigma_8-S_8$ tension, and the anomalies
present in the Planck results. Finally, we will give an overview of upgraded
experiments and next-generation space-missions and facilities on Earth, that
will be of crucial importance to address all these
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