New paper: Quantum transport equations

I recently submitted a new paper to the archive (where ‘pre-print’ copies of a paper go so everyone can access them, even while the peer review journal process proceeds). The title of the paper is ‘Transporting non-Gaussianity from sub to super-horizon scales‘.

The gist is this. During inflation (the accelerated expansion of the universe which we think occurred when the universe was extremely young), small quantum fluctuations on tiny scales are expanded to become classical undulations in the matter distribution and space-time geometry of the universe. These now classical fluctuations go on to collapse to form all structure in the universe (galaxies and clusters of galaxies). In the inflationary phase, when fluctuations behave in a quantum manner we call them sub-horizon perturbations, and when they are large enough to behave in a classical manner we call them super-horizon fluctuations. By measuring the properties of these fluctuations through observation, we learn about inflation.

But what properties do we care about? The undulations are spread out through the entire universe, and we don’t care about the precise value at any one point, what we care about are their statistical properties. For example, how likely it is to find a fluctuation with a given size, and how likely are large deviations from the ‘typical’ value.

During inflation these statistical properties can evolve, becoming constant sometime before or after inflation ends. I’ve been involved with developing techniques to track the evolution during inflation and beyond. So if one knows the statistics at some point in time, as we do for inflationary models, one can follow them thereafter. However, the methods I’ve been working on called ‘transport methods’ have so far only been applicable after the fluctuations become classical, restricting their use to problems where the quantum phase of evolution is simple. This new paper extends the methods to quantum sub-horizon scales.

There are a number of other methods around to perform the calculations this new method handles, but we think transport techniques have a number of advantages over them. Time will tell whether other researchers agree.


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