Cosmology, Inflation, and the Physics of Nothing by William H. Kinney

Author:William H. Kinney [Kinney, William H.]
Language: eng
Format: epub
Published: 2011-02-17T05:00:00+00:00

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so the Big Bang, a = 0, is a surface x = const. at τ = 0. Two points on a given τ = const. surface are in causal contact if their past light cones intersect at the Big Bang, τ = 0.

Figure 10.

Light cones in a FRW space, plotted in conformal coordinates, ds2 =

a2 dτ 2 − dx2 . The “Big Bang” is a surface at τ = 0. Points in the space can only be in causal contact if their past light cones intersect at the Big Bang.

So the natural expectation for the very early universe is that there should be a large number of small, causally disconnected regions that will be in poor thermal equilibrium. The central question is: just how large was the horizon when the CMB was emitted? Since the universe was about 300,000 years old at recombination, the horizon size then was about 300,000 light years. Each atom at the surface of last scattering could only be in causal contact (and therefore in thermal equilibrium) with with other atoms within a radius of about 300,000 light years.

As seen from earth, the horizon size at the surface of last scattering subtends an angle on the sky of about a degree. Therefore, two points on the surface of last scattering separated by an angle of more than a degree were out of causal contact at the time the CMB was emitted.

However, the CMB is uniform (and therefore in thermal equilibrium) over the entire sky to one part in 105. How did all of these disconnected regions reach such a high degree of thermal equilibrium?

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