Before we begin it is useful to be aware of the true nature of the Hubble Constant in SI units. This is for comparison purposes only and otherwise has nothing whatever to do with the new model that follows.
Hubble rate of recession 73 km s-1 Mpc-1. This breaks down to:
73000m s-1/ 30.857 x 1021m =
2.3675 x 10-18s-1
The distance to the edge of the observable universe without invoking relativity would be the speed of light (c) divided by this value.
c/2.3675 x 10-18 = 1.265 x 1026m = the edge of the observable universe.
It is accepted that electromagnetic radiation can travel through the eternity of the vacuum of space without suffering any effects apart from the tug of gravitational fields. However, the Heisenberg Uncertainty Principle allows for virtual electron positron pairs to continually appear & disappear in the vacuum of space. They are there for the incredibly short time of 3.2*10-22s yet that is long enough for a photon to travel around 30 times the classical electron radius. If a photon caused a recoil of the electron positron pair, then photons could lose energy and the recoil would generate the background radiation.
This may lead to an intrinsic problem in the measuring of energy/wavelength of photons.
From the quantum cosmology section, since we have established that the apparent expansion rate = 7.9*10-27m-1 or 7.9*10-29cm-1.
We now use this as our Z (red shift) predictor. We assume that this quantity affects our wavelength measurements.
Z = e (x.7.9*10^-27m^-1) -1; where x is the distance travelled in metres. The green line is the traditional Hubble line with an apparent recessional velocity of 73 km s-1 Mpc-1
Here we see that the function follows the Hubble line until around Z = 0.2 when it starts to leave the line curving up and giving a higher red shift than the Hubble line for the same distance. This is what has been found with supernova. At greater distances they are showing a higher red shift than that predicted by their brightness. With this model of the Universe it is just a natural feature of the way energy is lost exponentially due to quantum effects. There is no acceleration and no need for dark energy.
We can do a negative exponential as follows
E = E(0) e(-x.7.9*10^-27m); where x is the distance travelled in metres.
Here the gradient points to the apparent size of the observable universe on the x axis, which at the beginning points to around 1.265 x 1026 m which is equivalent to a recession speed of 73 km s-1 Mpc-1. At greater distances the gradient points to an apparent larger distance which equates with slower recession speeds. Since it is all illusory there is no need to consider relativistic effects or dark energy.
A fiddle? A coincidence? or something going on for which there is no experimental test? A free travelling photon would have to travel way beyond the solar system before it lost its first bit of energy. With it being an exponential, the relationship looks linear in our own region of the Universe but at greater distances the curve of the exponential kicks in, leading to the fact that the further we looked for our evidence of expansion the greater the radius of the observational universe would appear to become. This also leads to a Universe which gives the illusion of apparently expanding at a greater rate in our own locality than at greater cosmic distances which is in line with current supernova research. There is no need to wonder about dark energy and what is driving the expansion because it does not exist. The Universe only appears to be expanding faster in our own locality as a consequence of the model.
Question: How can this be true? The Universe has to be expanding, because the time for supernova to dim takes longer with increasing distance proving they are in a state of recession.
Answer: Could well be. However, following the above scenario, there is also an uncertainty in measuring energy and time dE.dt > h/4Pi. Therefore there would be a gradual loss of time information with distance leading to longer times and the illusion that time stands still at the edge of the observable Universe. Think of it as a very gradual loss of all information to do with energy, distance and time measurements that increases the further into the Universe that you observe. There is also a selection effect that may have influenced the results called the Malmquist bias. When allowance is made for this it appears that all evidence for time dilation vanishes. This is still up in the air at the moment.