The paper seems to be implying that at very small distances, the amount of energy can radically change the perceived length. For example, those of us that know about General Relativity know how spacetime can be warped dramatically by gravity. Thus, assuming that energy at such small distances can also warp lengths that would mean different wavelengths of light would behave differently -- And this would be most apparent in a very hot and dense Universe AKA the Big Bang. Obviously we can't notice it today because the Universe is much too cold for it to be apparent.
That is why it would radically change how the Universe would've 'started'. One of the side-effects would be a segregation of how groups of photons of different values would behave, and hence the term 'rainbow' is used. Think of us having to take the equations that describe photons and having to split them by wavelength for example. This is similar to what a prism does through refraction.
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