  We exhibit a varying speed of light (VSL) theory that implements the recently
proposed decaying speed of sound mechanism for generating density fluctuations.
We avail ourselves of bimetric VSL theories, where the speed of gravity differs
from that of light. We first show that a Dirac-Born-Infeld (DBI) type of
$K$-essence has the necessary speed of sound profile to produce (near)
scale-invariant fluctuations. We then examine the map between bimetric and
$K$-essence models: typically the bi-scalar connecting the two metrics is a
$K$-essence field in one of them. Remarkably, the DBI model is found to
perturbatively represent the minimal bimetric model, where the bi-scalar is
Klein-Gordon in the matter frame. But the full non-perturbative bimetric
structure is even simpler: the bi-scalar dynamics should be simply driven by a
cosmological constant in the matter frame, balanced by an opposite cosmological
constant in the gravity frame. Thus the problem of structure formation receives
an elegant and universal solution within bimetric VSL theories, which are known
to also solve the flatness and entropy problems and evade a plethora of
causality concerns.
