Abstract: The standard A Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few statistically significant tensions and anomalies were found in the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension between Planck data and weak lensing measurements and redshift surveys, in the value of the matter energy density Omega(m), and the amplitude sigma(8) (or the growth rate f sigma(8)) of cosmic structure. We list a few promising models for solving this tension, and discuss the importance of trying to fit multiple cosmological datasets with complete physical models, rather than fitting individual datasets with a few handpicked theoretical parameters.

Abstract: 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 S-8(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.

Abstract: Type Ia Supernovae (SNeIa) used as standardizable candles have been instrumental in the discovery of cosmic acceleration, usually attributed to some form of dark energy (DE). Recent studies have raised the issue of whether intrinsic SNeIa luminosities might evolve with redshift. While the evidence for cosmic acceleration is robust to this possible systematic, the question remains of how much the latter can affect the inferred properties of the DE component responsible for cosmic acceleration. This is the question we address in this work. We use SNeIa distance moduli measurements from the Pantheon and JLA samples. We consider models where the DE equation of state is a free parameter, either constant or time-varying, as well as models where DE and dark matter interact, and finally a model-agnostic parametrization of effects due to modified gravity (MG). When SNeIa data are combined with Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements, we find strong degeneracies between parameters governing the SNeIa systematics, the DE parameters, and the Hubble constant H-0. These degeneracies significantly broaden the DE parameter uncertainties, in some cases leading to O(sigma) shifts in the central values. However, including low-redshift Baryon Acoustic Oscillation and Cosmic Chronometer measurements, as well as CMB lensing measurements, considerably improves the previous constraints, and the only remaining effect of the examined systematic is a less than or similar to 40% broadening of the uncertainties on the DE parameters. The constraints we derive on the MG parameters are instead basically unaffected by the systematic in question. We therefore confirm the overall soundness of dark energy properties.