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Vacuum Energy and Inflation: 3. Newtonian Cosmology & GR

### Abstract

This is paper #3 in a series of four papers on vacuum energy and inflation. In paper #1 we discussed an example of what we have been calling vacuum energy . ^{1} It is an energy with negative pressure whose energy density remains constant in an expanding space. We showed that an energy density with these properties exists between the plates of a parallel plate capacitor. In paper #2 we discussed a model universe consisting of vacuum energy with a few galaxies added in as markers, so that we could observe the expansion of space. ^{2} We discovered that such a galaxy involved a huge release of gravitational potential energy, and we could easily calculate the rate of the Hubble expansion. Throughout, we used standard notation found in introductory physics, so that students could develop an intuition for the new concepts involved in an expanding space. In this, paper #3, we will use the notation of a scale factor a(t) to obtain equations similar to those derived from general relativity.

© 2013 American Association of Physics Teachers

Published online 08 October 2013

Article outline:

The Friedmann equation
Cosmological fluid equation
The acceleration equation