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Snowmass 2021 LoI: Determination of cosmic ray properties in the local interstellar medium with all-sky anisotropy observations

Propagation of Galactic cosmic rays (CR) in the interstellar medium (ISM) is among the unsolved problems in particle astrophysics. Interpretation of CR spectrum and composition measurements and their possible link to dark matter crucially relies on our understanding of CR propagation in the Galaxy. Several air shower experiments have measured a significant anisotropy of CRs in the TeV to PeV energy range. These observations hint to a complicated overlap of more than one cause: from the distribution of the CR sources in the Milky Way to the nature of such sources, from the turbulence properties of interstellar plasmas to the inhomogeneous nature of the interstellar medium. Coherent magnetic structures such as the heliosphere greatly influence the CR arrival direction distribution. It is necessary to account for and remove the heliosphere's distortion effects if we want to determine the pristine CR arrival direction distribution in the local interstellar medium (LISM), the environment surrounding the solar system up to the distance of particle mean free path. The recent availability of accurate all-sky maps of CR arrival direction distribution and the latest advancements in heliospheric modeling, make it possible to infer the CR pitch angle distribution in the LISM using a Liouville mapping technique. With the interstellar CR distribution, we can study the global characteristics of CR diffusion, tap into the properties of interstellar plasma turbulence, test the recent and local CR source hypothesis, and whether clumps of dark matter have a role in the observed CR observations. The study can lead to developments aiming to a better understanding of the heliosphere, particularly the boundary region with the ISM, and additional constraints on the LISM properties.