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The standard $Lambda$ 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 questions.
The current cosmological probes have provided a fantastic confirmation of the standard $Lambda$ Cold Dark Matter cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity a f
The standard $Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to th
A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent
In recent years, machine learning (ML) methods have remarkably improved how cosmologists can interpret data. The next decade will bring new opportunities for data-driven cosmological discovery, but will also present new challenges for adopting ML met
Two decades after its discovery, cosmic acceleration remains the most profound mystery in cosmology and arguably in all of physics. Either the Universe is dominated by a form of dark energy with exotic physical properties not predicted by standard mo