  This paper is dedicated to the memory of Dennis Sciama.
  Variable-Speed-of-Light (VSL) cosmologies are currently attracting interest
as an alternative to inflation. We investigate the fundamental geometrodynamic
aspects of VSL cosmologies and provide several implementations which do not
explicitly break Lorentz invariance (no "hard" breaking). These "soft"
implementations of Lorentz symmetry breaking provide particularly clean answers
to the question "VSL with respect to what?". The class of VSL cosmologies we
consider are compatible with both classical Einstein gravity and low-energy
particle physics. These models solve the "kinematic" puzzles of cosmology as
well as inflation does, but cannot by themselves solve the flatness problem,
since in their purest form no violation of the strong energy condition occurs.
We also consider a heterotic model (VSL plus inflation) which provides a number
of observational implications for the low-redshift universe if chi contributes
to the "dark energy" either as CDM or quintessence. These implications include
modified gravitational lensing, birefringence, variation of fundamental
constants and rotation of the plane of polarization of light from distant
sources.
