The MIGA project aims at demonstrating precision measurements of gravity with cold atom sensors in a large scale instrument and at studying the associated applications in geosciences and fundamental physics. The first stage of the project (2013-2018) will consist in building a 300-meter long optical cavity to interrogate atom interferometers and will be based at the low noise underground laboratory LSBB in Rustrel, France. The second stage of the project (2018-2023) will be dedicated to science runs and data analyses in order to probe the spatio-temporal structure of the local gravity field of the LSBB region, a site of high hydrological interest. MIGA will also assess future potential applications of atom interferometry to gravitational wave detection in the frequency band $sim 0.1-10$ Hz hardly covered by future long baseline optical interferometers. This paper presents the main objectives of the project, the status of the construction of the instrument and the motivation for the applications of MIGA in geosciences. Important results on new atom interferometry techniques developed at SYRTE in the context of MIGA and paving the way to precision gravity measurements are also reported.
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