University of Michigan - Department of Astronomy

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The Age of the Universe – Worksheets

Warm-up questions: These questions should be done before you start the activity. Your instructor may go through them as a class, in which case they will not be graded, but they wil be very useful for answering questions in the activity, so make sure you understand them.

  1. What does the Hubble constant measure?

  2. Compare 2 models at same size (i.e. d is the same for both models.) If v is greater in model A than in model B, will H0 be greater in model A, model B, or the same for both models?

  3. For the same two models, will model A be older, or model B, or will they both be the same ag (reminder, the age is 1/H0)?

  4. What is Omega Lambda a measure of?

  5. Compare 2 models at same size (i.e. d is the same for both models) but one has dark energy. Will the dark energy cause v to increase over time, decrease, or not affect v?

  6. If v increases over time, and we measure a value of H0 for now, would H0 have been larger, smaller, or the same in the past?

  7. Does having dark energy make the universe appear older, younger, or leave the age unaffected?


The “Standard” Cosmology

If we look at Hubble’s Law (v=H0 d) we notice that one over the Hubble constant H0 is just distance divided by velocity, which is also a time. Specifically this is the time it would take for any two objects in the universe to move a distance d from each other at an expansion velocity v. This should give us the age of the universe. If you have previously done the Hubble Law lab you have already shown how inverting Hubble’s constant gives the age of the universe. In this lab, you can use the Applet to find the age of the universe.

  1. Chose a reasonable value of the Hubble’s constant and enter this under Case 1 in the Cosmo Applet. Set ΩM = 0.0000001 (as close as you can get to 0) . The age of the Universe can be found by showing Plot Age and looking at where the line intersects Age at a redshift of z=0 (now). What age do you find? Be sure to include units.


  2. Calculating the age of the universe just using 1/ H0 (as we did in question 1) assumes that the matter in the universe does not affect the expansion and therefore the age of the universe. Of course, there is matter in the universe. Do you think the universe should be younger or older than the age found using 1/ H0? Explain your reasoning.



Now test your prediction from question 3.

For Case 1-5 input the same value of H0 and change the value of ΩM between 0.01 and 1 (you can leave the value of ΩL as zero). Record your observations in Table 1.

Table 1 - Effect of Omega M
Case # H0(km/s/Mpc) Omega Matter Age (Gyr)
Case 1      
Case 2      
Case 3      
Case 4      
Case 5      
  1. What happens to the age as the ammount of matter in the universe increases?




Open or Closed Universe

Recall that ΩM is ratio of the current density of the universe to the critical density that determines whether the universe will expand forever or eventually collapse. Densities of the universe above the critical density will result in a Closed Universe, which will eventually stop expanding. If the density is less than the critical density the Universe will continue to expand forever and is known as an Open Universe. The critical case, where the density of the universe exactly equals that critical density, the Universe will continue to expand forever, but just barely. This is the Flat Universe.

Set the Hubble Constant to 70 and choose three values of ΩM between 0.5 - 2.5 to represent a Closed, Open, and Flat universe. Display these in your Cosmo Applet window and switch to the “Plot Size” graph. Note the vertical axis is the ratio of the size at some other time (r) to the size now (r0). Enter your values of ΩM in table 2, and whether it represents a closed, open or flat universe.

Table 2: Open or Closed Universe
  ΩM Closed, Open, or Flat
Case 1    
Case 2    
Case 3    

If necessary, adjust the value of ΩMfor a Closed Universe that allows you to see when it will collapse again.

  1. Record the following information:
    1. What is your value of ΩM? _______
    2. What is the maximum size of this universe? ________
    3. What is its maximum age? ______
    4. What is its age when it starts to recollapse? ______

Modern Values of Omega Matter and Omega Lambda

Both the High-Z Supernova Search and the Supernova Cosmology Project (international collaborations of astronomers) found that the expansion of universe is in fact accelerating, rather than simply decelerating due to the attraction of gravity. To account for this acceleration factor, the cosmological constant, Lambda, has been introduced to our equations that describe the Universe.

  1. Do you think the universe should be younger or older if ΩL is included? Should the age increase or decrease as ΩL increases? Explain your reasoning.


Use the best values of H0=71 and ΩM= 0.3 for 4 cases. Set ΩL = 0 for the first case, then try different values of ΩL between 0.001 to 1.7 and record the resulting ages in Table 3.

Table 3 - Effect of Omega Lambda
Case # ΩL Age (Gyr)
Case 1 0  
Case 2    
Case 3    
Case 4    
  1. Does the age increase or decrease as ΩL increases?





  2. Observations and theory suggest that the universe is actually flat (OmegaTOTAL = 1.0). This is consistent with a value of ΩL of 0.7 if we have found all the matter (ΩM = 0.3).What is the current age of the universe for this model with a value of H0=71?

Updated: 10/19/12 by SAM

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