Angular Correlation

Many things were known before we were born, but far more important is what will become known after we are born. Stirring the pot is useful, and the post "Inflation Sinking" has drawn lively comment. We have a great positive post from Carl Brannen, an entire post devoted to critique that Starts With A Bang, and positive review on the new Carnival of Space!

For nigel and others: here is the early crude version of the angular correlation function. David Cline lectured on this to us at Stanford back in 2003. "Something funny," Dr. Cline titles this page, "the angular correlation function is nearly zero for angles beyond 60 degrees." A student kept his notes, calculated the red prediction curve without computers, and wrote it with marker pen. The typeface has been cleaned up, the data curves untouched. (Dr. Cline may have confused TE with TT curves, but that too is untouched.)

This graph measures the scale of density fluctuations in the cosmic microwave background. The old inflationary paradigm states that the Universe is flat, like the Earth. Density fluctuations should exist on all scales. These fluctuations can be modelled using spherical harmonics, the same maths we students used to model the hydrogen atom. When those fluctuations are added together they produce the "Inflation" curve. This prediction is ruled out by both COBE and WMAP experiments.

Theory predicts that the Universe is curved with radius R = ct, therefore the biggest possible fluctuation has peak-trough distance of 180 degrees. This prediction is very robust. You can model this curve in a calculator using sine waves, sawtooth or even square waves because all repeating functions can be modelled as sums of sine waves. Given the limits of marker pen, prediction fits the data quite closely.

Responding to everyone will take some time, but more comments are welcome. Please note that nobody here hates inflation, it has been acknowledged many times as a useful step. This work has been discussed personally with Alan Guth, who is considered a friend. We loved the Titanic, but it too slipped beneath density waves.