LCDM is alive and well!

The ΛCDM cosmological model, commonly referred to as the concordance model in cosmology, is highly effective in accurately explaining the majority of current cosmological observations. Nevertheless, this model faces several challenges when confronted with recent cosmological data of increased precision. The most significant statistical discrepancy arises from the disparity between the values of the Hubble constant (H0) derived from direct distance scale measurements and those obtained from observations of the cosmic microwave background (CMB). Additionally, there is a concern regarding the amplitude of matter fluctuations. Let's delve into the current state of affairs. First, I will show how this tension becomes apparent when we focus on a specific probe: galaxy clusters. By utilizing measurements derived from redshift space distortion (RSD), I will illustrate how we can mitigate the primary source of degeneracy. This analysis leads to the conclusion that the so-called "S_8 tension" can be substantially alleviated. Furthermore, I will highlight that the combination of several recent measurements from local probes yields a tightly constrained value for the current matter density, Ω_m. Remarkably, both S_8 and Ω_m are found to be in good agreement with the values deduced from the CMB within the framework of ΛCDM. Subsequently, I will address the Hubble tension by considering the possibility that certain determinations of the H0 value might be biased. I will statistically compare these "ΛCDM+ H0 bias" models to alternative cosmological models and demonstrate that the former can statistically outperform the extended models proposed thus far. Finally, I will illustrate that the recent Pantheon+ results, when combined with the inferred SH0ES value, lead to a value of the reduced cosmological density parameter, ω_m, which conflicts with the value inferred from the CMB for the ΛCDM model. Unfortunately, this situation does not show significant improvement even when considering alternative models devised to address the Hubble tension. This presents a new formulation of the Hubble tension, which is more demanding than the conventional metric.