Einstein's equivalence principle in cosmology
  We study physical consequences of the Einstein equivalence principle (EEP)
for a Hubble observer in FLRW universe. We introduce the local inertial
coordinates with the help of a special conformal transformation. The local
inertial metric is Minkowski-flat and materialized by a congruence of time-like
geodesics of static observers. The static observers are equipped with the ideal
clocks measuring the proper time that is synchronized with the clocks of the
Hubble observer. The local inertial metric is used for physical measurements of
spacetime intervals with the ideal clocks and rulers. The special conformal
transformation preserves null geodesics but does not keep invariant time-like
geodesics. Moreover, it makes the rate of the local time coordinate dependent
on velocity of the particle which makes impossible to rich the uniform
parameterization of the world lines of static observers and light geodesics
with a single parameter - they differ by the conformal factor of FLRW metric.
It tells us that the metric on the light cone is not Minkowski-flat but depends
on the scale factor of FLRW universe and it can be interpreted as a weak
violation of EEP for photons. The importance of this violation for
gravitational physics is that some of local experiments conducted with
freely-propagating electromagnetic waves may be sensitive to the Hubble
expansion. We show that the Hubble constant H can be measured within the solar
system by means of high-precision spacecraft Doppler tracking as a blue shift
of frequency of radio waves circulating in the Earth-spacecraft radio link. We
also analyze the behavior of the standing wave in a microwave resonator and
show that the standing wave is insensitive to the Hubble expansion.
