**[1] Cosmologies with varying light speed**We analyze a generalization of general relativity that incorporates a cosmic time variation of the velocity of light in vacuum, c, and the Newtonian gravitation “constant” G proposed by Albrecht and Magueijo. We find exact solutions for Friedmann universes and determine the rate of variation of c required to solve the flatness and classical cosmological constant problems. Potential problems with this approach to the resolution of the flatness and classical cosmological constant problems are highlighted. Reformulations are suggested which give the theory a more desirable limit as a theory of varying G in the limit of constant c and its relationship to theories with varying electron charge and constant c are discussed.

**[2] Light speed reduction to 17 metres per second in an ultracold atomic gas**Techniques that use quantum interference effects are being actively investigated to manipulate the optical properties of quantum systems1. One such example is electromagnetically induced transparency, a quantum effect that permits the propagation of light pulses through an otherwise opaque medium2,3,4,5. Here we report an experimental demonstration of electromagnetically induced transparency in an ultracold gas of sodium atoms, in which the optical pulses propagate at twenty million times slower than the speed of light in a vacuum. The gas is cooled to nanokelvin temperatures by laser and evaporative cooling6,7,8,9,10. The quantum interference controlling the optical properties of the medium is set up by a ‘coupling’ laser beam propagating at a right angle to the pulsed ‘probe’ beam. At nanokelvin temperatures, the variation of refractive index with probe frequency can be made very steep. In conjunction with the high atomic density, this results in the exceptionally low light speeds observed. By cooling the cloud below the transition temperature for Bose–Einstein condensation11,12,13 (causing a macroscopic population of alkali atoms in the quantum ground state of the confining potential), we observe even lower pulse propagation velocities (17?m?s−1) owing to the increased atom density. We report an inferred nonlinear refractive index of 0.18?cm2?W−1 and find that the system shows exceptionally large optical nonlinearities, which are of potential fundamental and technological interest for quantum optics.

**[3] Light speed variation from gamma-ray bursts**The effect of quantum gravity can bring a tiny light speed variation which is detectable through energetic photons propagating from gamma ray bursts (GRBs) to an observer such as the space observatory. Through an analysis of the energetic photon data of the GRBs observed by the Fermi Gamma-ray Space Telescope (FGST), we reveal a surprising regularity of the observed time lags between photons of different energies with respect to the Lorentz violation factor due to the light speed energy dependence. Such regularity suggests a linear form correction of the light speed v(E)=c(1−E/ELV), where E is the photon energy and ELV=(3.60±0.26)×1017GeV is the Lorentz violation scale measured by the energetic photon data of GRBs. The results support an energy dependence of the light speed in cosmological space.

**[4] Method for Constraining Light Speed Anisotropy by Using Fiber Optics Gyroscope Experiments**The Mansouri-Sexl theory is a well known test theory of relativity. Mansouri and Sexl dealt with the theory of the Michelson-Morley, Kennedy-Thorndike and Ives-Stilwell experiments but left out the very interesting Sagnac experiment. In the following paper we will present a novel way of detecting anisotropy effects in via a reenactment of the Sagnac experiment using fiber optic gyroscopes (FOG) where is the length of the fiber and is the angular speed of the FOG. We show how the fiber optics gyroscopes are used for constraining light speed anisotropy in the framework of the Mansouri-Sexl test theory. We also show an interesting amplification effect due to the use of the Mansouri-Sexl slow clock transport equations in conjunction with FOGs. Our paper is divided into four main sections: in the first one we give an overview of the Mansouri-Sexl test theory of special relativity, in the second one we give a historical perspective of the Sagnac experiment, in the third section we formulate the Mansouri-Sexl theory for the Sagnac experiment and we conclude with experimental setup and results.

**[5] 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.

**Reference**

**[1]**Barrow, J.D., 1999. Cosmologies with varying light speed.

*Physical Review D*,

*59*(4), p.043515.

**[2]**Hau, L.V., Harris, S.E., Dutton, Z. and Behroozi, C.H., 1999. Light speed reduction to 17 metres per second in an ultracold atomic gas.

*Nature*,

*397*(6720), pp.594-598.

**[3]**Xu, H. and Ma, B.Q., 2016. Light speed variation from gamma-ray bursts.

*Astroparticle Physics*,

*82*, pp.72-76.

**[4]**Sfarti, A., 2013. Method for constraining light speed anisotropy by using fiber optics gyroscope experiments.

*Physical Science International Journal*, pp.161-175.

**[5]**Gift, S.J., 2014. One-way Speed of Light Using Interplanetary Tracking Technology.

*Physical Science International Journal*, pp.780-796.