Test of the Einstein equivalence principle with spectral distortions in
  the cosmic microwave background
  The Einstein Equivalence Principle~(EEP) can be verified by the measurement
of the spectral distortions of the Cosmic Microwave Background (CMB). The
existence of energy-dependency in the cosmological redshift effect means the
EEP violation. Introducing the energy-dependent Friedmann-Robertson-Walker
metric motivated by rainbow gravity, we show that the energy-dependent redshift
effect causes the CMB spectral distortions. Assuming the simple
energy-dependent form of the metric, we evaluate the distortions. From the
COBE/FIRAS bound, we find that the deviation degree from the EEP, which is
comparable to the difference of the parameterized-post-Newtonian parameter
"gamma" in energy, is less than 10^{-9} at the CMB energy scale.
