Name: |

**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.

- What does the Hubble constant measure?

- 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 H
_{0}be greater in model A, model B, or the same for both models?

- 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/H
_{0})?

- What is Omega Lambda a measure of?

- 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?

- If v increases over time, and we measure a value of H
_{0}for now, would H_{0}have been larger, smaller, or the same in the past?

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

If we look at Hubble’s Law (**v=H _{0} d**) we notice that one over the Hubble constant

- Chose a reasonable value of the Hubble’s constant and enter this under Case 1 in the Cosmo Applet. Set Ω
_{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? Be sure to include units. - Calculating the age of the universe just using 1/ H
_{0}(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/ H_{0}? Explain your reasoning.

Now test your prediction from question 3.

For Case 1-5 input the same value of H_{0} and change the value of Ω_{M} between 0.01 and 1 (you can leave the
value of Ω_{L} as zero). Record your observations in Table 1.

Case # | H_{0}(km/s/Mpc) |
Omega Matter | Age (Gyr) |

Case 1 | |||

Case 2 | |||

Case 3 | |||

Case 4 | |||

Case 5 |

- What happens to the age as the ammount of matter in the universe increases?

Recall that Ω_{M} 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 Ω_{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 (r_{0}). Enter your values of Ω_{M} in table 2, and whether it represents a closed, open or flat universe.

Ω_{M} |
Closed, Open, or Flat | |
---|---|---|

Case 1 | ||

Case 2 | ||

Case 3 |

If necessary, adjust the value of Ω_{M}for a Closed Universe that allows you to see when it will collapse again.

- Record the following information:
- What is your value of Ω
_{M}? _______ - What is the maximum size of this universe? ________
- What is its maximum age? ______
- What is its age when it starts to recollapse? ______

- What is your value of Ω

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.

- Do you think the universe should be younger or older if Ω
_{L}is included? Should the age increase or decrease as Ω_{L}increases? Explain your reasoning.

Use the best values of H_{0}=71 and Ω_{M}= 0.3 for 4 cases. Set Ω_{L} = 0 for the first case, then try different values of Ω_{L} between 0.001 to 1.7 and record the resulting ages in Table 3.

Case # | Ω_{L} |
Age (Gyr) |
---|---|---|

Case 1 | 0 | |

Case 2 | ||

Case 3 | ||

Case 4 |

- Does the age increase or decrease as Ω
_{L}increases?

- Observations and theory suggest that the universe is actually flat (Omega
_{TOTAL}= 1.0). This is consistent with a value of Ω_{L}of 0.7 if we have found all the matter (Ω_{M}= 0.3).What is the current age of the universe for this model with a value of H_{0}=71?

Updated: 10/19/12 by SAM

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