Relativity and Cosmology Blog

Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

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Inflation or no Inflation

Posted December 31, 1998 5:00 PM by Jorrie

"The universe appears to be uniform in all directions because the speed of light is the universal speed limit.

We can only see as far as light has traveled in our visible universe, and as a consequence, everything looks equidistant from us, or from every other point of view."

Not quite. You are apparently referring to the Cosmic Microwave Background radiation, which we observe as the inside surface of a sphere, but its uniformity in temperature comes from something that happened before the present day expansion started. We are not sure what that was, because it cannot be observed, but a rapid inflation over a short period of time is still the best buy in cosmology.

To the right is a log-log-scale expansion graph, showing the early epochs, before and after inflation quite dramatically. The horizontal scale is log(t/tPlanck) and the vertical is log(r/rPlanck), where ±r is the increasing light-travel-distance for two bundles of CMB photon, coming from opposite sides of the CMB sphere to our telescopes in the center.

Those photons presently have the same black-body temperature of some 2.7K, to within 1 part in 105. If we (naively) linearly extrapolate the distance between the photon bundles shown back to time t=tPlanck (10-43 seconds), using Einstein's theory of general relativity, we find that the locations from where they came, were still quite far apart and could hence not have interacted with each other to equalize the temperature to the degree that we observe.

This is where the theory of inflation comes in. It allows all the source areas of the CMB radiation to be on top of each other for enough time to allow equalization of the temperatures. Then inflation happened around t=10-33s (10 units on the log scale after the origin at 10-43s) and rapidly (exponentially) expanded distances everywhere by at least 35 log-units in just 2 log-units of time. This left us the (almost) uniform CMB that we observe today.

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