Go to the Cosmology JavaLab at Case Western Reserve University. Click on Applet in the menu on the left. A new window should open, in which you can enter cosmological parameters (at the present epoch): the Hubble constant, H₀, the mean matter density as a fraction of the critical density, Ω_m, and the energy density of the cosmological constant, Ω_Λ.

Enter the following four cosmological models, all with the same value of H₀ = 70 (km/s)/Mpc:

Select Plot size from the pull-down menu and click on the plot — you should get a plot of the scale factor, R(t), as a function of time. The Hubble constant, H₀, is the same for all four, but the age of the Universe at the present epoch is different.

1. Describe the differences in the expansion histories of these four universes; what is qualitatively different about Case 4?
2. Rank the above cosmological models in the order of their modern age, from youngest to the oldest.
3. Estimate the ages of the four models from the graph.

Now consider a different four models, all with Ω_m = 1 and Ω_Λ = 0. Take H₀ = 500 (Hubble's original value), 100 (the value preferred by some observers in the 1970s, 70 (the value preferred by most cosmologists today), and 55 (the value according to Allan Sandage).

4. Estimate the ages of the four models from the graph obtained with Plot size.

Select Plot Age from the pull-down menu to see the relation between redshift and the time elapsed from when the light was emitted until now when it is detected at that redshift.

5. Suppose someone tells you that there is a new galaxy discovered with a redshift of z =3.0 and that its stars appear to be approximately 2 billion years (Gyr) old with an uncertainty of 200 million years (i.e., 10%). Assuming this observation is valid, which of the original four cosmological model(s) can be ruled out? You can enter data points on the plot by using the Edit Data Points button.

This assignment, which is similar to what cosmologists do to rule out cosmological models, is a modification of one originated by Dr. Andrey Kravtsov of the University of Chicago.