Name: Partner(s): Day/Time: Version: Disc

The Age of the Universe – Worksheets

Warm-up questions: These questions should be done before you start the activity. If you can't answer them, go back and read the introduction again or talk to your instructor. Ask your instructor if you should turn in the answers to these questions.

1. What does the Hubble constant measure?
   
2. How is redshift related to the age of the universe (in general, you don't need to know the formula)?
   
3. What can stop the expansion of the universe, at least on small scales?
   
4. What is the fate of the universe if it is Flat?
   
5. What is the critical density of the universe (definition, not a number)? How is it related to the quantity we call Omega Matter?
   
6. When we say that a closed universe will someday recollapse, what does that mean?
   
7. When we say the universe is accelerating, do we mean the expansion is speeding up or slowing down?
   
8. What does the cosmological constant (Lambda) refer to and why is important for understanding the fate of the universe?
   
9. What is Omega Lambda a measure of?

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 Omega_M = 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?
   
   
   
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. Why would the fact that there is matter in the Universe change the age you would get from inverting Hubble’s constant (Hint: H₀ = the current rate of expansion, is constant?)?
   
   
   
   
   
   
3. Since we know there is matter in the universe, we know that the actual age of the universe is not just 1/ H₀.Do you think the universe would 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 Omega_M between 0.01 and 1 (you can leave the value of Omega_L as zero). Record your observations in Table 1.

4. How does the age of the universe change, as you increase the density of matter in the Universe?
   
   
   
   

Open or Closed Universe

Recall that Omega 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 Omega_M 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). Pick a value of Omega_M for a Closed Universe that allows you to see when it will collapse again.

5. What is your value of Omega_M? What is the maximum size of this universe? What is its maximum age?
   
   
   
   
6. What age will it start collapsing? How can you tell?

Observed H₀ and Omega Matter

Now set all of the values of Omega_M to the current best estimate: Omega_M = 0.3. Change the values of H₀ to fall between 50 and 100 km/s/Mpc. Record the results in Table 2.

7. How does increasing the value of H₀ change the age of the universe?
   
   
   
8. Hubble Key Project results using Cepheid variable star distances suggest that the best estimate of H₀ is 71 km/s/Mpc. Observations of clusters of galaxies suggest that Omega_M = 0.3. Given this cosmology, what is the age of the universe?
   
   
   
   

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. For H₀=71 and Omega_M= 0.3, try different values of Omega_L between 0.001 to 1.75) and record the resulting ages in Table 3.

Table 3 - Effect of Omega Lambda

9. How does adding a non-zero cosmological constant effect the age of the universe? Explain why you would expect this, given that the cosmological constant was added to the model to explain the acceleration of the universe. (Hint: If the expansion of the universe is accelerating, then it must have been expanding at a slower rate in the past.)
   
   
   
   
   
   
   
10. Observations and theory suggest that the universe is actually flat (Omega_TOTAL = 1.0). This is consistent with a value of Omega_L of 0.7 if we have found all the matter (Omega_M = 0.3).What is the current age of the universe for this model with a value of H₀=71?
    
    
11. For a quasar with a redshift of z=6, how old was the universe when the light left that quasar, given the parameters from the previous question? What is the look-back time for that quasar?

Last updated: 3/13/08