We perform a new test of Einstein's Equivalence Principle which, for the first time, extends to very early cosmological epochs (we have studied its validity in 80% of the history of the Universe). The Einstein Equivalence Principle is essential for generalizing physical laws in the presence of gravity. Our test of the Equivalence Principle is based on one of Einstein's classical predictions: the gravitational redshift of photons. This test has been accurately put into practice in our Solar System and in some stars in our Galaxy (e.g. Sirius B). However, so far it has not been applied to
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