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Abstract Theories of modified gravity generically violate the strong equivalence principle, so that the internal dynamics of a self-gravitating system in freefall depends on the strength of the external gravitational field (the external field effect). We fit rotation curves (RCs) from the SPARC database with a model inspired by Milgromian dynamics (MOND), which relates the outer shape of an RC to the external Newtonian field from the large-scale baryonic matter distribution through a dimensionless parametere_N. We obtain a > 4σstatistical detection of the external field effect (i.e.e_N> 0 on average), confirming previous results. We then locate the SPARC galaxies in the cosmic web of the nearby universe and find a striking contrast in the fittede_Nvalues for galaxies in underdense versus overdense regions. Galaxies in an underdense region between 22 and 45 Mpc from the celestial axis in the northern sky have RC fits consistent withe_N≃ 0, while those in overdense regions adjacent to the CfA2 Great Wall and the Perseus−Pisces Supercluster returne_Nthat are a factor of two larger than the median for SPARC galaxies. We also calculate independent estimates ofe_Nfrom galaxy survey data and find that they agree with thee_Ninferred from the RCs within the uncertainties, the chief uncertainty being the spatial distribution of baryons not contained in galaxies or clusters. 

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