  Deformed special relativity (DSR) is one of the possible realizations of a
varying speed of light (VSL). It deforms the usual quadratic dispersion
relations so that the speed of light becomes energy dependent, with preferred
frames avoided by postulating a non-linear representation of the Lorentz group.
The theory may be used to induce a varying speed of sound capable of generating
(near) scale-invariant density fluctuations, as discussed in a recent Letter.
We identify the non-linear representation of the Lorentz group that leads to
scale-invariance, finding a universal result. We also examine the higher order
field theory that could be set up to represent it.
