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 $n=-0.0033\pm 0.0045$ 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 $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) 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.

Figure 1

The 68.3% and 95.4% confidence regions in the $w_{x0}\text{−}{\mathrm{\Omega }}_{m0}$ parameter space for VSLDE, which are constrained by the combined observational data of SNIa, CMB, OHD, and BAO. The red asterisk indicates the best-fit point.

Figure 2

Same as Fig. 1 but for the $n\text{−}{w}_{x0}$ parameter space.

Figure 3

The reconstruction of speed of light $c(z)$. The central red solid line is the best-fit value of $c(z)$. Top and bottom lines are the errors of reconstructed $c(z)$ in the $1\sigma$ confidence level.

Figure 4

The reconstruction of EoS of dark energy $w_x(z)$. The central red solid line is the best-fit value of $w_x(z)$. The shaded regions are the errors of reconstructed EoS within $1\sigma$ confidence level.

Figure 5

The reconstruction of $Om(z)$ diagnostic. The central red solid line is the best-fit curve of $Om(z)$ in the VSLDE. The blue dashed line represents the $Om(z)$ in the spatially flat $\mathrm{\Lambda }\mathrm{CDM}$. The shaded area shows the $1\sigma$ error region in the VSLDE.