If one divides a change in proper distance by the interval of cosmological time where the change was measured (or takes the derivative of proper distance with respect to cosmological time) and calls this a "velocity", then the resulting "velocities" of galaxies or quasars can be above the speed of light, c. Such superluminal expansion is not in conflict with special or general relativity nor the definitions used in physical cosmology. Even light itself does not have a "velocity" of c in this sense; the total velocity of any object can be expressed as the sum v tot = v rec + v pec where v rec is the recession velocity due to the expansion of the universe (the velocity given by Hubble's law) and v pec is the "peculiar velocity" measured by local observers (with v rec = a ˙ ˙ ( t ) χ χ ( t ) and v pec = a ( t ) χ χ ˙ ˙ ( t ) , the dots indicating a first derivative), so for light v pec is equal to c (− c if the light is emitted towards our position at the origin and + c if emitted away from us) but the total velocity v tot is generally different from c. Even in special relativity the coordinate speed of light is only guaranteed to be c in an inertial frame ; in a non-inertial frame the coordinate speed may be different from c. In general relativity no coordinate system on a large region of curved spacetime is "inertial", but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" in which the local speed of light is c and in which massive objects such as stars and galaxies always have a local speed smaller than c. The cosmological definitions used to define the velocities of distant objects are coordinate-dependent – there is no general coordinate-independent definition of velocity between distant objects in general relativity. How best to describe and popularize that expansion of the universe is (or at least was) very likely proceeding – at the greatest scale – at above the speed of light, has caused a minor amount of controversy. One viewpoint is presented in Davis and Lineweaver, 2004.