  It is generally believed that inflationary cosmology explains the isotropy,
large scale homogeneity and flatness as well as predicting the deviations from
homogeneity of our universe. We show that this is not the only cosmology which
can explain successfully these features of the universe. We consider anew and
modify a model in which local Lorentz invariance is spontaneously broken in the
very early universe, and in this epoch the speed of light undergoes a first or
second order phase transition to a value ~ 30 orders of magnitude smaller,
corresponding to the presently measured speed of light. Before the phase
transition at a time t ~ t_c, the entropy of the universe is reduced by many
orders of magnitude, allowing for a semiclassical quantum field theory
calculation of a scale invariant fluctuation spectrum. After the phase
transition has occurred, the radiation density and the entropy of the universe
increase hugely and the increase in the entropy follows the arrow of time
determined by the spontaneously broken direction of the vev <\phi^a>_0. This
solves the enigma of the arrow of time and the second law of thermodynamics. A
new calculation of the primordial Gaussian and adiabatic fluctuation spectrum
is carried out, leading to a scale invariant scalar component of the power
spectrum. We argue that there are several attractive features of VSL theory
compared to standard inflationary theory, and that it provides an alternative
cosmology with potentially different predictions.
