  The cosmological constant problem has become one of the most important ones
in modern cosmology. In this paper, we try to construct a model that can avoid
the cosmological constant problem and have the potential to explain the
apparent late-time accelerating expansion of the universe in both luminosity
distance and angular diameter distance measurement channels. In our model, the
core is to modify the relation between cosmological redshift and scale factor
for photons. We point out three ways to test our hypothesis: the supernova time
dilation; the gravitational waves and its electromagnetic counterparts emitted
by the binary neutron star systems; and the Sandage--Loeb effect. All of this
method is feasible now or in the near future.
