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The Einstein Equivalence Principle~(EEP) can be verified by the measurementof the spectral distortions of the Cosmic Microwave Background (CMB). Theexistence of energy-dependency in the cosmological redshift effect means theEEP violation. Introducing the energy-dependent Friedmann-Robertson-Walkermetric motivated by rainbow gravity, we show that the energy-dependent redshifteffect causes the CMB spectral distortions. Assuming the simpleenergy-dependent form of the metric, we evaluate the distortions. From theCOBE/FIRAS bound, we find that the deviation degree from the EEP, which iscomparable to the difference of the parameterized-post-Newtonian parameter"gamma" in energy, is less than 10^{-9} at the CMB energy scale.

Test of the Einstein equivalence principle with spectral distortions in the cosmic microwave background