Introduction
The scientific community considered the speed of light as truly isotropic relative to every reference frame, therefore including the Earth, as is supported by Special Relativity (SR) but only by a stipulation.
Because the isotropy can only be apparent, because light is a wave phenomenon which therefore needs a medium to manifest itself, and therefore its speed can only be isotropic relative to the medium and therefore not also relative to a celestial object, such as the Earth, which moves relative to the medium. As I demonstrated in the article on the speed of light that I published on this website. However, the GPS system can only work based on appearance, because it is not possible to know the precise speed of the Earth relative to the medium, which would be necessary to make it work based on reality. So, in this case, it is well justifiable to consider the speed of light isotropic relative to the Earth, but for calculations only, not because it actually is. In truth, the fact that GPS works based on appearances can be considered a kind of gift of nature that man has managed to exploit
A hundred years ago, based on the appearance in the calculation of the speeds of celestial objects as a function of their cosmological redshift, the scientific community applied the formula of the Doppler effect which considers the Earth at rest and all celestial objects in motion, according to which when the redshift value is greater than unity, the speed exceeds that of light and, therefore, is incompatible with the SR itself.
But later, when redshifts with values greater than one and then increasingly higher were observed, the scientific community had to repeatedly change its interpretation, until it finally considered it to be the scale factor of the expansion of the Universe, as it actually is.
And then, based on its interpretations, it hypothesized that the expansion of the Universe is accelerating.
According to my theory, instead, the Universe is composed of an infinite number of space quanta that tend to expand and therefore cause the Universe to expand as well. But as they expand, the force with which they tend to expand also decreases, thus slowing the speed at which the Universe expands.
Consequently, the expansion of the Universe can only slow down, although it is not yet known by how much.
However, even for my theory, the cosmological redshift indicates the scale factor of the expansion of the Universe, but, at least in my opinion, the observational data currently available should only allow us to determine the duration of light’s journey. This is, however, very important, because it would allow us to determine the epoch relative to the scale factor. Therefore, by combining the scale factors of various observations and therefore of various epochs, it would be possible to obtain a diagram showing the evolution of the Universe’s expansion and, therefore, also verify whether the expansion was slowing down and even by how much. Or whether it was actually accelerating, as the scientific community claims.
However, as I wrote in a specific article of mine published on this website, there are various indications that support the argument that the expansion of the Universe is slowing down, and now I would like to present a formula that, through observations of type Ia supernovae, should allow us to deduce the evolution of the expansion of the Universe over time.
Formula for obtaining the epoch relative to the scale factor, using observations of type Ia supernovae
Type Ia supernovae are celestial objects with a high and well-defined luminosity, making them visible even at billions of light-years away. They can be used as standard candles, that is, to calculate their distance from Earth based on their observed apparent luminosity.
Furthermore, using the formula I will present below, it should also be possible to obtain the duration of the light’s travel and, therefore, the epoch relative to the scale factor.
Thus, using the thousands of observations of Type Ia supernovae already available, it should be possible to obtain a diagram that associates the scale factors of the expansion of the Universe with their corresponding epochs.
In conclusion, it should be possible to obtain the evolution of the expansion of the Universe.
The basic starting formula represents the ratio between the absolute brightness (L) and the apparent brightness (l), and is the following:
l = L / ((4 * π * T**2) * (1 + z)**3))
The denominator includes two factors:
1) (4π • T²) corresponds to the surface area of a sphere with a radius that corresponds to the distance travelled by the photons of light relative to the locations they pass through and therefore also to the duration of the journey (T for time). This is because as they move, the photons are distributed as if on the surface of an increasingly larger sphere, as its radius lengthens. But only the distance travelled by the photons relative to the locations they pass through must be considered, and not the distance by which the locations they pass through have moved away from the location of the galaxy, due to the expansion of space, as this displacement is considered in the second factor.
2) (1 + z)³ corresponds to the expansion of space that occurred during the photons’ journey, which is uniform throughout the Universe, including those where the supernova photons passed. The value of the expansion must be cubed, as it is a volumetric expansion, which therefore occurs in three spatial dimensions. It practically corresponds to the scale factor of the expansion of the Universe relative to the time of the photons’ departure.
From this formula I derived the formula for finding the duration of the photon’s journey, which would allow us to know the epoch in which the photons have left and therefore to consider the factor 1 + z as the scale factor relative to that epoch.
Here it is:
T = rad((L / l) * (1 / ((4 * π) * (1 + z)**3))
In this formula, T represents both the distance travelled by light in billions of light years and the duration of the total journey in billions of years and, as I wrote above, it would allow us to match the scale factor with the relative epoch and, therefore, to obtain a graph with the history of the expansion of the Universe, which should allow us to verify whether it is truly accelerating.
In presenting the formula, I used the conditional verb, as I have not verified it using real data because I don’t have them, but I hope that astrophysicists who have them will do so. In practice, all the data are available from observations, namely the absolute luminosity (which is the same for all supernovae), and the apparent luminosity and cosmological redshift, which are those detected by observations of each supernova.