Cosmology and Cosmic Structure Evolution

The vertical axis gives the distance to a galaxy in billions of light years (two black curves) or the lookback time in billions of years (red curve) for the cosmological parameters presently thought to govern the expansion of the present universe, as functions of the galaxy redshift, z. The lookback time measures how long light we observe now has been traveling - that is, how long ago the light we see observe now left the galaxy. A lookback time of 10 billion years means that we observe the galaxy as it was 10 billion years ago. Or, in other words, the lookback time is how long the light from a distant galaxy we observe now took to travel from there and then to here and now. The distance at the "cosmic now" (by observers at rest relative to the Hubble flow, i.e., comoving observers) is the radial co-moving coordinate distance (equal to the proper distance in a spatially flat geometry), and appears in the Hubble Relation, v_rec = H_od. The "distance then" is sometimes called the emission distance, and is a measure of how far away the galaxy was then when the light we see now left the galaxy. The ratio of these two distances, radial co-moving coordinate to emission distance, is simply 1+z for spatially flat geometries. For example, a galaxy with a measured redshift of 1.0 was 5.5 billion light years away at the time of emission of the light we see today, is now 11 billion light years away, and we observe it now as it was 7.9 billion years ago. Notice that the emission distance never exceeds approximately 5.89 billion light years near a redshift of 1.65, and then diminishes at greater redshift. This distance asymptotes toward zero at infinite redshift, meaning that all objects we now can observe were once relatively near to us (although you should keep in mind that the first galaxies likely began forming between redshifts of 30 and 10). This emission distance can in principle be measured by comparing the angular sizes of a class of objects of similar physical size, and so it is often called the angular diameter distance. The distance now asymptotes to about 47.9 billion light years, meaning that objects that have ever been above our cosmic horizon are now no further away than this in curved space-time. The lookback time, of course, aysmptotes to the present age of the universe at very large z; here 14 billion years (blue line). At very small z, d(now), d(then), and c x t(lookback) are very nearly the same, as expected. This last one, c x t(lookback), does not actually pertain to any useful distance to the galaxy in an expanding universe, but is unfortunately quoted as THE distance in the mass media. What should be said instead is that we observe the galaxy now as it was t(lookback) years ago. Still confused? That's ok, but now try this link, and Wikipedia has an excellent article, as well. All points in the above graph and mentioned here were generated courtesy of Ned Wright's cosmology calculator (the advanced version here). Generate your own plot at iCosmo.

Links to Cosmology and Cosmic Structure Evolution