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We implement and explore high-dimensional generalized dark matter (HDGDM) with an arbitrary equation of state as a function of redshift as an extension to Λ cold dark matter. Exposing this model to cosmic microwave background, baryon acoustic oscillations, and supernova data, we demonstrate that the use of marginalized posterior distributions can easily lead to misleading conclusions on the viability of a high-dimensional model such as this one. We discuss such pitfalls and corresponding mitigation strategies, which can be used to search for an observationally favored region of the parameter space. We further show that the HDGDM model in particular does show promise in terms of its ability to ease the Hubble tension once such techniques are employed, and we find interesting features in the best-fitting equation of state that can serve as an inspiration for future model building. 

Models which address both the Hubble and S8 tensions with the same mechanism generically cause a pre-recombination suppression of the small scale matter power spectrum. Here we focus on two such models. Both models introduce a self-interacting dark radiation fluid scattering with dark matter, which has a step in its abundance around some transition redshift. In one model, the interaction is weak and with all of the dark matter whereas in the other it is strong but with only a fraction of the dark matter. The weakly interacting case is able to address both tensions simultaneously and provide a good fit to a the Planck measurements of the cosmic microwave background (CMB), the Pantheon Type Ia supernovae, and a combination of low and high redshift baryon acoustic oscillation data, whereas the strongly interacting model cannot significantly ease both tensions simultaneously. The addition of high-resolution cosmic microwave background (CMB) measurements (ACT DR4 and SPT-3G) slightly limits both model's ability to address the Hubble tension. The use of the effective field theory of large-scale structures analysis of BOSS DR12 LRG and eBOSS DR16 QSO data additionally limits their ability to address the S8 tension. We explore how these models respond to these data sets in detail in order to draw general conclusions about what is required for a mechanism to address both tensions. We find that in order to fit the CMB data the time dependence of the suppression of the matter power spectrum plays a central role. 

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