4.1 the Flatness Problem

Module 4.1: Alan Guth — The Flatness Problem
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MODULE 4.1: The Flatness Problem Summary

It turns out that the value of Ω is approximately equal to 1.

– This poses a puzzle—in the standard Big Bang theory, the value Ω=1 is an unstable equilibrium point.

– Small deviations from this value would have significant effects on the nature and curvature of the universe.

– If Ω had been exactly equal to 1, it would be 1 forever. But since we measure it to be almost equal to 1 today, the instability implies it must have been substantially closer to 1 in the early universe.

Cosmologists wondered how the initial density came to be so closely fine-tuned to this “special” value.

– For the value of Ω to be anywhere near 1 today, its value would have to be tuned fantastically close to 1 in the early universe.

– At one second after the Big Bang, Ω would have had to equal 1 to an accuracy of 15 decimal places.

– Inflation proposes a solution for this “fine-tuning” problem. Since inflation makes gravity repulsive, the evolution of Ω also changes.

– Ω is driven rapidly toward 1 in the inflationary model. It is driven so rapidly that its initial value could have been almost anything. Yet, this mechanism almost always overshoots in accuracy, predicting a much flatter universe than we measure today.

However, there was another problem: Ω was not originally measured to be equal to 1.

– Until 1998, astronomers measuring Ω found its value to be approximately 0.2, much different than the predicted 1.

– The missing ingredient was dark energy, a material with negative pressure.

– When the contributions of dark energy are included, the observed value of Ω is very close to 1.

– The latest observations, measured by the Planck satellite, indicate Ω to be approximately 1.0010 ± 0.0065.