Tests for the Expansion of the Universe
  Almost all cosmologists accept nowadays that the redshift of the galaxies is
due to the expansion of the Universe (cosmological redshift), plus some Doppler
effect of peculiar motions, but can we be sure of this fact by means of some
other independent cosmological test? Here I will review some recent tests: CMBR
temperature versus redshift, time dilation, the Hubble diagram, the Tolman or
surface brightness test, the angular size test, the UV surface brightness limit
and the Alcock--Paczy\'nski test. Some tests favour expansion and others favour
a static Universe. Almost all the cosmological tests are susceptible to the
evolution of galaxies and/or other effects. Tolman or angular size tests need
to assume very strong evolution of galaxy sizes to fit the data with the
standard cosmology, whereas the Alcock--Paczynski test, an evaluation of the
ratio of observed angular size to radial/redshift size, is independent of it.
