The Cosmic Time in Terms of the Redshift
  In cosmology one labels the time t since the Big Bang in terms of the redshift of light emitted at t, as we see it now. In this Note we derive a formula that relates t to z which is valid for all redshifts. One can go back in time as far as one wishes, but not to the Big Bang at which the redshift tends to infinity. 
Moshe Carmeli, John G. Hartnett, Firmin J. Oliveira