**[1] New varying speed of light theories**

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying-c, dispelling the myth that the constancy of c is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a colour-dependent speed of light; varying-c induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ‘doubly special’ relativity has emerged as a VSL effective model of quantum space–time, with observational implications for ultra-high energy cosmic rays (UHECRs) and gamma ray bursts. Some recent work on the physics of ‘black’ holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in c. Finally, we describe the observational status of the theory. The evidence is currently slim—redshift dependence in the atomic fine structure, anomalies with UHECRs, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight but not insurmountable. We conclude with the observational predictions of the theory and the prospects for its refutation or vindication.

**[2] cc is the speed of light, isn’t it?**

Theories for a varying speed of light have been proposed as an alternative way of solving several standard cosmological problems. Recent observational hints that the fine structure constant may have varied over cosmological scales have given impetus to these theories. However, the speed of light is hidden in many physics equations and plays different roles in them. We discuss these roles to shed light on proposals for varying speed of light theories. We also emphasize the requirements for attaining consistency of the resulting equations, when what was previously a constant is made a dynamical variable.

**[3] Time varying speed of light as a solution to cosmological puzzles**

We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light c is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the standard big bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function c(t). The large entropy inside the horizon nowadays can also be accounted for in this scenario.

**[4] One-way Speed of Light Using Interplanetary Tracking Technology**

Light transmission in the Sun-Centered Inertial (SCI) frame is considered within a flat space-time metric of relativity theory. It is shown that this metric which is used to derive the Langevin metric that generates the accurate clock synchronization algorithm used in the Global Positioning System (GPS), also predicts one-way light speed anisotropy in an inertial frame that contradicts the principle of light speed constancy. This finding is tested and confirmed in the SCI frame using the range equations employed in the tracking of planets and spacecrafts moving within our solar system. These equations are based on the observation that light travels in the SCI frame at a constant speed c and have been extensively tested and rigorously verified. The results suggest a modification of the Lorentz Transformations that yields new transformations that are consistent with the observed light speed anisotropy and which better accord with the physical world.

**[5] Two-way and One-way Vacuum Speed of Light under the Membrane Paradigm**

The discovery of cosmic microwave background radiation (CMB) by Wilson and Penzias defines a rest frame in the sense of Newton’s absolute space. This fact is one of the reasons why brane worlds moved into the focus of interest. Membrane theory (CM) uses the cosmological model of a 4-dimensional thin membrane, expanding in hyperspace. A homogeneous vector field acts perpendicularly from outside onto the membrane and causes, this way, curvature of space and gravitation. The membrane defines an absolute Newtonian space, and forces small changes of Special Relativity (SR). The most important difference between CM and SR is the introduction of a cross contraction of moving bodies.

Reference

**[1] **Magueijo, J., 2003. New varying speed of light theories. *Reports on Progress in Physics*, *66*(11), p.2025.

**[2] **Ellis, G.F. and Uzan, J.P., 2005. c is the speed of light, isn’t it?. *American journal of physics*, *73*(3), pp.240-247.

**[3] **Albrecht, A. and Magueijo, J., 1999. Time varying speed of light as a solution to cosmological puzzles. *Physical Review D*, *59*(4), p.043516.

**[4] **Gift, S.J., 2014. One-way Speed of Light Using Interplanetary Tracking Technology. *Physical Science International Journal*, pp.780-796.

**[5] **von Weber, S. and von Eye, A., 2017. Two-way and one-way vacuum speed of light under the membrane paradigm. *Physical Science International Journal*, pp.1-17.