The reason I am not considering a linear relationship is that we do not see a great change of the speed of light at this point. Though this may not be the exact equation, until we have found with some evidence for any relationship and the data to work with this is the closes I can come to its approximation.

The idea in its simplest for would be this:

At the beginning there is not time passage and no speed of light, so both are zero…
At the first moment of time (We will for this example call a second) there is to first formation of space time and now a distance that light (We will for this example just consider all phenomena that travels at the speed of light), (We will for this example consider call this distance a meter).

So at | Time | Speed |
| 0 | 0 |
| 1 | 1 |
| 4 | 2 |
| 9 | 3 |
| 25 | 5 |
| 100 | 10 |

So trying to calculate the variation on the assumption that the beginning was 14 billion years ago.
| 4.421088e+17 | 299,792,458 |

T*X=C*C (X being the variation from our seconds to meters conversion ratio) and T=(C*C)/X
(4.421088e+17)*X = (8.987551787368176e+16)

X = (8.987551787368176e+16)/(4.421088e+17) = 0.2032882355512529

So for 1 meter of change it would take: 2949432441.941939 seconds
1 Millimeter then takes 2949432.441941939 or in days 34.13694955951318
These calculations are only based on the approximation of the time factor, but if they are even close enough there should be a millimeter change in the speed of light going faster at about 35 days.

Setting up the experiment:

This could be done with a large 10 meter by 10 meter enclosure that can be kept under environmental control to try and eliminate any variations do to temperature. It would be sealed and vacuumed. Sensors place inside and out to insure that conditions at the time of testing are the same.
We then place a laser at one corner to beam strait across. This then hits a mirror at a slight angle to bounce the light back but off to the side by a centimeter. Here it is again reflected but by a mirror that covers the rest of this side, back to the other side. The angle of inclination would remain and another mirror covering the other side would again bounce the light back. Each bounce would move the light beam over about 1 centimeter till it reached the end of the box. At this point the beam can either be detected or another mirror at an angle can send it back down to reiteration of bounces back two the corner of the laser were it can be detected, giving it 2 cycles though the apparitions. Within all of this a physical measurement of the enclosure and each bounce can be known and the total distance the light traveled calculated. Variation due to light fading from the multiple reflections or other factors may come into consideration. In all the measurement does not have to be exact to what we consider the speed of light, as the test will be made in all likelihood on the earth were other factors may enter in from gravity to having stray atoms in the chamber because of a imperfect vacuum. But his is not a factor within this test as were are looking for a variation of the speed over time and not the speed itself. As long as all conditions are kept standard this test may show whatever results are correct. One of the most important pieces of this experiment is the timer. Here we can use a tunable gigahertz digital oscillator. This also being hooked up to a oscilloscope so to be calibrated to an exact frequency forever test. The faster this oscillator the better to get any indication of variation, but also within the confines of the equipment from the starting pules and laser ignition to the detection. Again if all parameters remain constant then any change in the speed of light can be recorded and see if this variation is a function of time. We can run the test 10 times a day to take an average. Then every day for some time. It should take no more than a year to get the data on whether or not there is any variation that fits this theory.

Why it happens: The expansion of space and/or the Higgs field.
I will try to explain this as best I can with an imagination exercise. It has often been used as a method to show how the universe is expanding by placing the galaxies on the surface of a balloon and then inflating it for show how everything is moving apart. This simple example will also work for me in this explanation. So we have a balloon of such and such size. On this balloon we mark to points, A and B of course. Now, there is a certain distance between these points. Let’s imagine that there is some interaction of the nature of the speed of light, so at point A we send a photon to point B. It takes a certain amount of time. No, if while that photon is traveling the balloon is inflated a bit, then it would either take a bit more time or have to compensate for this by traveling a bit faster. As you can see in my theory it will just travel a bit faster with the expansion. This theory would give some credence to the idea that the medium (Space or the Higgs field, or even an old idea of the ether) was expanding. Though at this point that may be another assumption, the only way to know is with more valid test.

That is all I will say at this point about this theory as it should be enough to be considered or not. If you do consider it I have other ideas you may be interested in.