Cosmology with Variable Physical Constants

The speed of light is taken to be a constant in a vacuum. This forms the basic tool for the principle of General Covariance, which asserts that, all laws of Physics should take the same form in all frames of reference. Without putting inflation into consideration, the theory of varying speed of light (VSL) would solve basic problems of cosmology in the early universe. Furthermore, the constants, Λ and G that occurred in the Friedmann Equations may not have been real constants in the early universe but have some variation with the universe scale factor. We obtained solutions to the cosmological model of flat FRW Universe where Λ and G are taken to be variables. We used the solution to obtain deceleration parameter and state finder parameter. We also found out that the Hubble constant will be a constant if and only if Λ = 0 but conversely, it is inversely proportional to the cosmic time. For VSL, we have used the power law where we have taken and . For , we obtained the expansion rate of the universe and for by numerical solution we observed that the expansion of the universe accelerating for flat space geometry where . Also, we assumed that ̇, this enabled us to obtain the expression for the age of the universe for this model. We also studied the model of Linearly Varying Deceleration Parameter which reveals that the universe evolves from a big bang and ends with a big rip. Keywords: Deceleration Parameter, Friedmann Equation, FRW Metric, CMB, Equation of State.