Model I- Fixed space

There will be a redshift in the spectral lines of each galaxy related to its recession velocity. For this model, this redshift is called the Doppler shift. The redshift, z, is defined as z=(l-l_o)/l_o so that z+1=l/l_o which is simply the observed wavelength at our telescope of a particular spectral line divided by the emitted wavelength (the wavelength measured in the laboratory). For low velocities and hence low values of z, this leads to the relation v=cz. For velocities of recession approaching that of light we need to use the equations of special relativity in this model to get the relativistic Doppler effect equation tying the recession velocity, v, to the redshift, z. The equations are:

v=c((z+1)²-1)/((z+1)²+1)--------(1)
z+1=((1+v/c)/(1-v/c))^1/2--------(1a)

There is a problem with this model. Consider a galaxy rushing away from us at a constant velocity of very nearly the speed of light. Light that it emitted when the universe was half as old as it is now would just be getting to us now and we could not have a lookback time, t_lb, (t_lb=t_o-t_e), greater than half the age of the universe. We find we are able to see much further back in time than this. The cosmic microwave background radiation, CMBR, coming to us from all directions was emitted when the universe was very young (something like 300,000 years after the big bang or about 1/50,000 of its present age), and we can detect this radiation now. It is this background radiation that greatly strengthened the arguments for the big bang theory. We are also able to look back now to galaxies as they were when the universe was less than 10% of its present age. Also, consider a light packet just reaching us now. In this first simple model that packet coming toward us, if it started at nearly the birth of the universe, would have been some 14 billion light years away from us at the big bang - but the big bang model assumes that all of the presently observable region of space was in a very tiny volume at that time.