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Abstract In recent years discrepancies have emerged in measurements of the present-day rate of expansion of the universe H 0 and in estimates of the clustering of matter S 8 . Using the most recent cosmological observations we reexamine a novel model proposed to address these tensions, in which cold dark matter disintegrates into dark radiation. The disintegration process is controlled by its rate Q  = αℋρ ddm , where α is a (constant) dimensionless parameter quantifying the strength of the disintegration mechanism and ℋ is the conformal Hubble rate in the spatially flat Friedmann-Lemaître-Robertson-Walker universe and ρ ddm is the energy density of the disintegrating cold dark matter. We constrain this model with the latest 2018 Planck temperature and polarization data, showing that there is no evidence for α≠ 0 and that it cannot solve the H 0 tension below 3σ, clashing with the result obtained by analyzing the Planck 2015 temperature data. We also investigate two possible extensions of the model in which the dark energy equation-of-state parameter w ≠ -1. In this case it is possible to combine Planck data with the SH0ES measurement, and we demonstrate that in both these models the H 0 tension is resolved at the 1σ level, but the condition w ≠ -1 exacerbates the S 8 tension. We also demonstrate that the addition of intermediate-redshift data (from the Pantheon supernova type Ia dataset and baryon acoustic oscillations) weakens the effectiveness of all these models to address the H 0 and S 8 tensions. 

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. These new methods will become increasingly important in the coming years as the volume of survey data continues to increase, and as the degeneracy between predictions of different physical models grows. There are several perspectives on the divergences between the values of cosmological parameters, such as the model-independent probes in the late Universe and model-dependent measurements in the early Universe, which we cover at length. The White Paper closes with a number of recommendations for the community to focus on for the upcoming decade of observational cosmology, statistical data analysis, and fundamental physics developments