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Abstract Quasars (QSOs) are extremely luminous active galactic nuclei currently observed up to redshift z = 7.642. As such, they have the potential to be the next rung of the cosmic distance ladder beyond Type Ia supernovae, if they can reliably be used as cosmological probes. The main issue in adopting QSOs as standard candles (similarly to gamma-ray bursts) is the large intrinsic scatter in the relations between their observed properties. This could be overcome by finding correlations among their observables that are intrinsic to the physics of QSOs and not artifacts of selection biases and/or redshift evolution. The reliability of these correlations should be verified through well-established statistical tests. The correlation between the ultraviolet and X-ray fluxes developed by Risaliti & Lusso is one of the most promising relations. We apply a statistical method to correct this relation for redshift evolution and selection biases. Remarkably, we recover the the same parameters of the slope and the normalization as Risaliti & Lusso. Our results establish the reliability of this relation, which is intrinsic to the QSO properties and not merely an effect of selection biases or redshift evolution. Hence, the possibility to standardize QSOs as cosmological candles, thereby extending the Hubble diagram up to z = 7.54. 

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