1. Observational constraint on the varying speed of light theory Speaker: Qi Jing-Zhao Advisor: Prof. Liu Wen-Biao Department of Physics, Beijing Normal University

2. INTRODUCTION  Varying speed of light theory has been put forward to explain some cosmological problems, such as horizon, flatness and cosmological singularity problems.  However, the VSL cosmology is excluded by mainstream physics because it makes much of modern physics which depends on a constant speed of light to be rewritten. Moreover, it also faces a number of other detailed issues.  Thus, whether the speed of light is varying cannot be judged by theoretical analysis but by investigations of the observational data.

3. The varying speed of light theory  Generally, one can introduce the time-variable c(t) in the metric or in the Friedmann equations.  Friedmann equations:  The metric:

4.  Although in the reference [1], they believe that introduction of c(t) in the metric does not change the physics by a coordinate transformation: [1] B. A. Bassett, S. Liberati, C. Molina-Paris, and M. Visser, Physical Review D 62, 103518 (2000). In this transformation: In order not to change the reality of cosmic time, we would like to investigate the behavior of VSL theory in the normal cosmic time frame. Thus, introduction of the time-variable c(t) in the metric is more fundamental than in the Friedmann equations which is used by many research of VSL theory.

5.  We will just think about a spatial flat FRW universe, namely k = 0, for simplicity. New Friedmann equations:

6. Where c 0 is the current value of speed of light, n is a constant. And then, the conservation equation is We can define the equation of state (EoS) as:

7. Solving this differential equation, we have where ρ0 is the present value of total energy density. If we only consider the contribution of dark energy and matter, namely,, where denotes matter density and is dark energy density.

8. Observational data  Type Ia supernovae  Cosmic microwave background  Baryon acoustic oscillation  Observational H(z) data

9. Constraining the parameter of vsl theory

10. FIG. 3. The reconstruction of speed of light c(t). The central red solid line is the best-fit value of c(t). Top and bottom lines are the errors of reconstructed c(t) in 68.3% confidence level. FIG. 4. The reconstruction of EoS of dark energy wx(z). The central red solid line is the best-fit value of wx(z). The shaded regions are the errors of reconstructed EoS within 68.3% confidence level.

11. Difference between VSLDE and ΛCDM  Now, we apply an effective geometrical diagnostic, Om(z), to directly show the difference between the VSLDE and ΛCDM. Om(z) is defined as

12. In Fig. 5, we reconstruct the geometrical diagnostic Om(z) at 68.3% confidence level, and find that the VSLDE and ΛCDM cannot be discriminated. It is main because that the key factor of varying speed of light theory n is so feeble. To some extent, the speed of light may be a constant with high significance.

13. CONCLUSION The varying speed of light (VSL) theory is controversial. We devote ourselves to test 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 (CMB). We select the common form with the contribution of dark energy and matter. The combined observational data show a much trivial constraint at 68.3% confidence level, which indicates that the speed of light may be a constant with high significance. We also introduce the geometrical diagnostic Om(z) to show the difference between the VSLDE and ΛCDM model. The result shows that the current data are difficult to differentiate them. All the results show that the observational data favor the constant speed of light. Arxiv: 1407.1265

14. Outlook  Many research of VSL theory introduced the time-variable in the Friedmann equations. However, we introduced the time-variable c(t) in the metric, and then obtained the new form of Friedmann equations. Can the VSL theory still solve these cosmological problems?  we adopt a widely used form of VSL, i.e.,.The conclusion is under this assumption. Therefore, it must be careful to extrapolate our conclusions. The VSL theory in other forms should be investigated in future work.

15. Thanks