Properties Spanning the Full History

Concordance model parameters. All columns are linear in time, with redshift marked on the left. Columns 1 and 2 are complementary, giving age and look-back time. Column 3 gives the scale factor a = 1/(1 + z). Column 4 gives the density, assuming it goes like a-3. Column 5 gives the CMB temperature, which increases as 1/a. Column 6 is the velocity history of a galaxy currently at 1 Mpc. It is called the comoving Hubble parameter, H(z)/(1 + z), where H(z) is the normal Hubble parameter (1/a)(da/dt). The full velocity history is also shown in graphical form [here]. Finally, column 7 is the angular size of a fixed physical size of 10 kpc (roughly, a galaxy diameter). Notice how it reaches a minimum of ~1 arcsec at z ~ 1.5.

 

More parameters of the concordance model. The first three columns give the three kinds of distance: lookback time, dlbt = c(to - te); distance at time of emission, dp(te); and current (comoving) distance, dp(to). The next three columns show three different aspects of cosmic volume. Column 4 gives the comoving volume in 106 Mpc3 for a region of solid angle 1 deg2 and depth dz = 0.1. Notice how it increases but then decreases as dz corresponds to less and less comoving distance. Column 5 gives the percentage of the entire comoving volume visible out to the particle horizon. One needs to go to z ~ 6 to enclose ~50% of the total volume. Column 6 is similar but for physical (not co-moving) volume. This time, z ~ 1.2 encloses ~50% of the volume, and the recent redshift surveys to z ~ 0.2 include ~2% of the entire volume. The final column simply gives the wavelength and band of Lyman alpha.

Figures made for this course.