Quantum fluctuations of fields are inherent across all energy and temperature scales, with significant implications during low temperatures, particularly near absolute zero. The fluctuations that contributed to the universe's structure originated from zero-point fluctuations of the inflaton field. The size of these fluctuations is often associated with the Planck scale, but this is more a matter of convention than a strict requirement, as fluctuations can occur at various wavelengths. The evolution of these fluctuations from sub-Planckian to super-Planckian scales is a key issue known as the "trans-Planckian problem," highlighting the current gaps in our understanding of quantum gravity.
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failexam said:Why do quantum fluctuations of fields arise at high energies and temperatures?
failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?
It's actually the reverse.failexam said:Why do quantum fluctuations of fields arise at high energies and temperatures?
The particular fluctuations you seem to be talking about are zero-point fluctuations of the inflaton field. If you want a really in-depth look, here's one source:failexam said:What is the mathematical formulation of these quantum fluctuations?
I think that's more of an assumption than anything. How big they were depends more upon the properties of inflation: the fluctuations would have been close to the size of the horizon at the time of inflation. But we don't know what that horizon size was yet because we don't know for sure what the energy scale of inflation was.failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?
If by "size" you mean wavelength, then there is no assumption that they must be Planck size, though that is generally how they are treated (i.e. you can have a quantum fluctuation of any wavelength). The thing is that larger wavelength fluctuations spend less time within the horizon during inflation and so are amplified much less than Planck sized fluctuations. How to evolve the fluctuation from sub-Planckian to super-Planckian scales is known as the "trans-Planckian problem", since, lacking a UV-complete theory of gravity, we don't actually know how sub-Planckian fluctuations evolve.failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?