Dynamical Tests

Dynamical Test: Mass and Expansion Rate of the Universe

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.



How do we go about this exercise?

  • We then compare the expansion rate to the escape speed.



    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:

    Explicitly, the critical density for the Universe is

    where H is the Hubble constant denoted by Ho 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:

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