Hubble Deep Field Image

The idea for small z 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 and so assume one of the above solutions by acquiring redshifts, distances, and masses of nearby objects in the universe.

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How do we go about this exercise?

• We first determine the rate at which the Universe expands from Hubble's law (which then tells us how much mass, radiation, and dark energy is needed to make Ω = 1).

• We then try to make a complete accounting of the components of the Universe.

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Sounds simple, Let's do it. The expansion rate of the Universe is given by the Hubble constant H_o. The critical density is then

ρ_c = 3H_o²/(8πG)

where G is the gravitational constant. For convenience, we define Ω as

Ω = (ρ/ρ_c)

We see that if Ω > 1, the Universe is closed and if Ω < 1, the Universe is open. If Ω = 1, the Universe is flat.

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To determine the ultimate fate of the Universe we must find Ω. To do so, we do the following: we find the expansion rate of the Universe, the Hubble constant, to determine the critical density, and then we find the various components of the Universe, the mass, the photons, and the dark energy.

• Expansion Rate of the Universe--Find Redshifts and distances to galaxies
• Weight of the Universe--Find masses of each component of the Universe

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