Observational constraint on the varying speed of light theory

The varying speed of light theory is controversial. It succeeds in explaining some cosmological problems, but, on the other hand, it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devote ourselves to testing whether the speed of light is varying from the observational data of the type Ia supernova, baryon acoustic oscillation, observational H(z) data, and cosmic microwave background. We select the common form c(t) = c(0)a(n) (t) with the contribution of dark energy and matter, where c(0) is the current value of speed of light and n is a constant, and consequently we construct a varying speed of light dark energy model (VSLDE). The combined observational data show a trivial constraint n = -0.0033 +/- 0.0045 at 68.3% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time variable c(t), we find that the speed of light almost has no variation for redshift z < 10(-1). For high-z observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of 10(-2). We also introduce the geometrical diagnostic Om(z) to show the difference between the VSLDE and Lambda cold dark matter (Lambda CDM) models. The result shows that the current data make it difficult to differentiate them. All the results show that the observational data favor the constant speed of light.