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In summary, the resent observational results in cosmology strongly suggest that we live in a universe that is spatially flat, expanding at an accelerated rate, homogeneous and isotropic on large scales, and is approximately 13 billion years old. The expansion of the universe is described by Eq. (63), and its metric by Eq. (64). We have seen that roughly 96% of the matter and energy in the universe consists of cold dark matter and the cosmological constant. We now know basic facts about the universe much more precisely than we ever have. However, since we cannot speak with confidence about the nature of dark matter or the cosmological constant, perhaps the most interesting thing about all of this is that knowing more about the universe has only shown us just how little we really understand.

As mentioned previously, the most common view of the cosmological constant is that it is a form of vacuum energy due, perhaps, to quantum fluctuations in spacetime. [5] However, within the context of general relativity alone there is no need for such an interpretation; Lambda is just a natural part of the geometric theory. [40] If, however, we adopt the view that the cosmological constant belongs more with the energy-momentum tensor than with the curvature tensor, this opens up a host of possibilities including the possibility that Lambda is a function of time. [41]

In conclusion, it is also important to state that although this paper emphasizes what the recent results say about our present universe, these results also have strong implications for our understanding of the distant past and future of the universe. For an entertaining discussion of the future of the universe see Ref. 42. Concerning the past, the results on anisotropies in the CMB have provided strong evidence in favor of the inflationary scenario, which requires a Lambda-like field in the early universe to drive the inflationary dynamics. To quote White and Cohn [17], "Of dozens of theories proposed before 1990, only inflation and cosmological defects survived after the COBE announcement, and only inflation is currently regarded as viable by the majority of cosmologists."


We would like to especially acknowledge (and recommend) the excellent website of Dr. Wayne Hu. [43] This resource was very useful in helping us to learn about the physics of CMB anisotropies. We are also grateful to Dr. Manasse Mbonye for making several useful suggestions.

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