A varying-c cosmology

We develop a new model for the Universe based on two key assumptions: first, the inertial energy of the Universe is a constant, and second, the total energy of a particle, the inertial plus the gravitational potential energy produced by the other mass in the Universe, is zero. This model allows the speed of light and the total mass of the Universe to vary as functions of cosmological time, where we assume the gravitational constant to be a constant. By means of these assumptions, the relations between the scale factor and the other parameters are derived. The Einstein equation, by making it compatible with varying-$c$, is used and the Friedmann equations in this model are obtained. Assuming the matter content of the Universe to be perfect fluids, the model fixes $\gamma$ to be 2/3. That is, the whole Universe always exhibits a negative pressure. Moreover, the behavior of the scale factor is the same for any value of the curvature. It is also shown that the Universe began from a big bang with zero initial mass and expands forever even with positive curvature, but it is always decelerating. At the end, solutions to some famous problems, mainly of the standard big bang model, and an explanation for the observational data about the accelerating Universe are provided.