Varying Light Velocity as a Solution to the Problems in Cosmology

In earlier published work, it was proposed that light speed was larger in the early Universe by 30 orders of magnitude compared to its presently observed value. This change in the speed of light is associated with a spontaneous breaking of local Lorentz invariance in the early Universe, associated with a first order phase transition at a critical time $t=t_c$. This solves the horizon problem, leads to a mechanism of monopole suppression in cosmology and can resolve the flatness problem. After the critical time $t_c$, local Lorentz (and diffeomorphism) invariance is restored and light travels at its presently measured speed. We investigate solutions of the field equations in the spontaneously broken phase and study further the flatness problem and the cosmological constant problem. The entropy is shown to undergo a large increase as the light velocity goes through a phase transition. A scale invariant prediction for microwave background fluctuations originating at the time of the phase transition is discussed.