The idea for the dynamical tests is straightforward. We try to determine if the initial kick given to the Universe was large enough to cause the Universe to exceed its escape velocity.

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How do we go about this exercise?

• We first determine the escape speed for the Universe,
  The escape speed is determined by how strongly gravity retards the expansion; we can get a measure of the escape speed by measuring the mass of the Universe

• We then determine how fast the Universe is expanding from the Hubble Law,
  The Hubble constant H_o tells us how fast the Universe is expanding.

We then compare the expansion rate to the escape speed.

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Sounds simple, Let's do it. The escape escape is determined by the amount of mass in the Universe and by how close together is the mass: the critical density for our Universe can be determined by measuring the rate at which our Universe is expanding. This when compared to the actual density in the mass will indicate whether our Universe is open, closed, or flat.

For a closed Universe, if the Universe has:

• A high rate of expansion ==> need a lot of slowing down ===> large density

• A slow rate of expansion ==> need less slowing down ===> smaller density

Explicitly, the critical density for the Universe is

where H is the Hubble constant denoted by H_o for the value measured at the present epoch and G is the gravitational constant. For convenience, we define Omega as

We see that if Omega > 1, the Universe is closed and if Omega < 1, the Universe is open. If Omega = 1, the Universe is flat. We determine Omega from:

• Expansion Rate of the Universe
• Weight of the Universe

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