Testing the equivalence principle: from the lab to the Galactic Center
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The Einstein equivalence principle is at the heart of the theory of General Relativity. This principle is not based on theoretical considerations but rather on experimental facts and is violated in numerous unification scenarios, Dark Matter models and Dark Energy models. In this colloquium, I will review the motivations to test the equivalence principle and present recent experimental results that search for a breaking of the equivalence principle. First, I will focus on preliminary results of the MICROSCOPE space-mission that provide the best test of the universality of free fall and of the Lorentz invariance. Second, I will show how laboratory experiments involving atomic clocks can be used to search for scalar Dark Matter candidates. Finally, I will present two recent tests of the equivalence principle using measurements of short-period stars orbiting the supermassive black hole in our Galactic Center. The first one is related to the measurement of the gravitational redshift of the star S0-2/S2. The second one consists in a search for a variation of the fine structure constant around our Galactic Center.