The lookback time t_{L} to an object is the difference between the age t_{0} of the Universe now (at observation) and the age t_{e} of the Universe at the time the photons were emitted (according to the object). It is used to predict properties of high-redshift objects with evolutionary models, such as passive stellar evolution for galaxies. Recall that E (z) is the time derivative of the logarithm of the scale factor a (t); the scale factor is proportional to (1 + z), so the product (1 + z) E (z) is proportional to the derivative of z with respect to the lookback time, or
(Peebles 1993, pp. 313-315; Kolb & Turner 1990, pp. 52-56, give some analytic solutions to this equation, but they are concerned with the age t (z), so they integrate from z to ). The lookback time is plotted in Figure 6.
Figure 6. The dimensionless lookback time t_{L} / t_{H} and age t / t_{H}. The three curves are for the three world models, (_{M}, _{}) = (1, 0), solid; (0.05, 0), dotted; and (0.2, 0.8), dashed. |