  During the inflationary phase of the early universe, quantum fluctuations in
the vacuum generate particles as they stretch beyond the Hubble length. These
fluctuations are thought to result in the density fluctuations and
gravitational radiation that we can try to observe today. It is possible to
calculate the quantum-mechanical evolution of these fluctuations during
inflation and the subsequent expansion of the universe until the present day.
The present calculation of this evolution directly exposes the particle
creation during accelerated expansion and while a fluctuation is larger than
the Hubble length. Because all fluctuations regardless of their scale today
began as the vacuum state in the early universe, the current quantum mechanical
state of fluctuations is correlated on different scales and in different
directions.
