Variance in speed of light While discussing this question (Does light have an unending journey?) I stumbled on the fact that light's speed is constant only in inertial frame.
What I happened to do was add up the expansion of universe to the theory. It goes as follows: 
Suppose from a source we emit a photon, at the same time, we (source) are moving away from the point of launch and so is the point that too with acceleration, now lets consider the moment when we are so far from the point of fire that the distance between the 2 points (source and firing point) is so much that the space with their respect to each other is moving with speed more than speed of light, certainly since the points are also constantly being separated they have a relative velocity of separation which just happens to be more than speed of light, now by the time the fired photon must have travelled even further and its speed now with respect to the source must be greater than speed of light. 
Can this be taken as a prove for the variance of speed of light from inertial frames?
 A: You're assuming, incorrectly, that general relativity has a unique and natural way of describing the velocity of cosmologically distant objects. That isn't the case. There isn't any such definition, because velocity is a vector, and parallel transport of vectors is path-dependent.
A: Current, standardized definition of distance is based on the assumption that speed of light is constant, inertial frame or not. (See, for instance, wikipedia's page on metre).
Nevertheless, hypothesis of variable speed of light sometimes is used in cosmology. Note, that this is one of possible explanations of observations and not the most widespread. 
Edit. Upon reading OP's comments I would like to rephrase Ben Crowell's argument:
For curved spacetimes distance between two objects can grow at a rate exceeding the speed of light and that in no way violates general relativity and its postulate about the universality of speed of light. One way to understand this is to look at the space-time diagrams. Let's look at the one from Ned Wright's Cosmology Tutorial

Small red triangles are the light-cones for given point -- that is if we draw space-time trajectory of an object at that point it will be inside the light-cone for that point, but the slant of the trajectory (which corresponds to the growth rate of distance) could be greater than the slant of the light-cone for some other point.
