### Analytical Solution to FRW Metric with Variable Speed of Light

#### Abstract

According to the principle of general covariance, the laws of physics are the same in all reference frames. The controversial theory of the Varying Speed of Light (VSL) contradicts the principle of general covariance. Fortunately the VLS theory explains some crucial issues in cosmology such as Lorentz variance, biometric theories, locally Lorentz variance, cosmological constant problem, horizon* *and flatness* *problems. Also, recent astronomical observations from quasar show that the fine structural constant depends on redshift and therefore, varies with cosmological time. In other to harness this fascinating and published knowledge, two models where used in this work. 1. Cosmology with variables c; here the Friedmann-Robertson-Walker (FRW) is used in the Einstein field equation with variable c and Λ terms to obtain the scale factor, which shows the continuous exponential expansion of the universe. 2. Variation of the speed of light as a function of the scale factor of the universe; here we obtained: a good approximation to estimate the current age of the universe. The scale factor of the universe depends its content given by the equation of state parameter ω. We obtained the deceleration parameter in terms of the Hubble parameter. We arrived at a conclusion that the universe was decelerating at ω = 1, accelerating at ω = 1/3 and the Hubble parameter diverges at the beginning and end of the universe.

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