Cosmic vacuum and light speed
The first, by lead author Marcel Urban of the Université du Paris-Sud, looks at the cosmic vacuum, which is often assumed to be empty space. The laws of quantum physics, which govern subatomic particles and all things very small, say that the vacuum of space is actually full of fundamental particles like quarks, called "virtual" particles. These matter particles, which are always paired up with their appropriate antiparticle counterpart, pop into existence and almost immediately collide. When matter and antimatter particles touch, they annihilate each other.
Photons of light, as they fly through space, are captured and re-emitted by these virtual particles. Urban and his colleagues propose that the energies of these particles -- specifically the amount of charge they carry -- affect the speed of light. Since the amount of energy a particle will have at the time a photon hits it will be essentially random, the effect on how fast photons move should vary too.
As such, the amount of time the light takes to cross a given distance should vary as the square root of that distance, though the effect would be very tiny -- on the order of 0.05 femtoseconds for every square meter of vacuum. A femtosecond is a millionth of a billionth of a second. The speed of light has been measured over the last century to high precision, on the order of parts per billion, so it is pretty clear that the effect has to be small.