How Flat Space Cosmology Models Dark Energy

Equations of Flat Space Cosmology (FSC) are utilized to characterize the model’s scalar temporal behavior of dark energy. A table relating cosmic age, cosmological redshift, and the temporal FSC Hubble parameter value is created. The resulting graph of the log of the Hubble parameter as a function of cosmological (or galactic) redshift has a particularly interesting sinuous shape. This graph greatly resembles what ΛCDM proponents have been expecting for a scalar temporal behavior of dark energy. And yet, the FSC R h = ct model expansion, by definition, neither decelerates nor accelerates. It may well be that apparent early cosmic deceleration and late cosmic acceleration both ultimately prove to be illusions produced by a constant-velocity, linear-ly-expanding, FSC universe. Furthermore, as discussed herein, the FSC model would appear to strongly support Freedman et al. in the current Hubble tension debate, if approximately 14 Gyrs can be assumed to be the current cosmic age.

DOI: 10.4236/jmp.2020.1110091 1494 Journal of Modern Physics few hundred million years of cosmic expansion. We should then have a remarkably accurate "moving picture" computer simulation of the history of that portion of the universe we can now observe.
When astrophysicists concern themselves with the velocities of galactic separation on scales greater than those of the local clusters held together by gravity and dark matter, they are studying the Hubble parameter and its tight correlation with cosmological redshift. When the Hubble parameter is characterized as a "snapshot" of the universe at a particular point in cosmic time ( [1]. The ongoing temporal (i.e., "moving picture") studies of the universe are expected to show that, over the great span of cosmic time, the Hubble parameter is, in fact, scalar in some way. The first evidence of this became apparent in 1998, with studies of Type Ia supernovae [2], which revealed the presence of dark energy. Thus, it became apparent that there is an unseen energy, presumably within the cosmic vacuum, which prevents gravitational deceleration of the expanding universe. We now know that universal expansion, at present, is either occurring at constant velocity (as treated by R h = ct cosmological models) or very slightly accelerating (as claimed by ΛCDM concordance model cosmologists). Both types of cosmological models are still viable at the present time [3]- [8].
Observations in the coming decade may well identify which model is superior.
Flat Space Cosmology (FSC) is perhaps the most successful R h = ct model to date [9]. It predicts a current Hubble parameter H 0 value of 66.893 km•s −1 •Mpc −1 , fitting with the 2018 Planck Collaboration consensus. It also predicts the COBE CMB dT/T anisotropy ratio of 0.66 × 10 −5 . A book chapter summary of FSC is now freely available online [10]. In contrast to ΛCDM cosmology (which incorporates observations ad hoc but makes relatively few falsifiable predictions), the FSC equations provide for very specific predictions, which can falsify the model if proven wrong. Remarkably, to date, the FSC model has not been falsified.
The purpose of the current report is to show how FSC models the temporal dark energy expansion of the universe. We show in great detail the scalar nature of the FSC Hubble parameter, so that it can be compared to the observations to be made in the coming decade.

Methods
Previously-published equations of FSC, relating cosmological (or galactic) redshift z, temporal cosmic temperature T t , temporal cosmic radius R t , the associated temporal Hubble parameter H t , the currently-observed Hubble parameter H o , the currently-observed cosmic temperature T o , and cosmic age t, are brought together in the Results section in order to derive the parameter values given in Table 1 and Figure 1.

Results
The following two FSC equations are useful for deriving the model relationships between a given cosmological (or galactic) redshift z and the associated temporal Hubble parameter H t : The first equation relates the redshift to the temporal cosmic temperature T t and the currently-observed cosmic temperature T o [11]. The second equation relates the temporal cosmic temperature T t to the temporal cosmic radius R t [12].
Recalling the FSC Hubble parameter definition (H t = c/R t ), rearrangement and substitution gives: To convert the H t term from reciprocal seconds (s −1 ) to the conventional Using T 0 = 2.72548 K, this simplifies to: Equations (5), (6) and (7) can then be used to create Table 1 and Figure 1.
The last two z values given in Table 1 are two of the highest galactic redshifts observed to date.

Discussion
Proponents of the ΛCDM concordance model of cosmology, and R h = ct model cosmologists, are currently in a pitched battle to establish which model is more accurate with respect to observations and predictions. As documented in recent publications [13] [14], FSC is a realistic linear light-speed cosmic expansion model which can also be considered a modified Milne "empty universe" model.  Notice also that this graph correlates a redshift z value of 1.0 with a cosmic scale of 0.5 times the current scale. This is true for FSC as well as ΛCDM, although the two models differ slightly with respect to the current cosmic age.
In ΛCDM cosmology, the post-inflationary cosmological vacuum energy density is assumed to be a constant. This is not an absolute requirement of general relativity, so long as the vacuum energy density is scalar according to 2 2 3 t H c Λ = .
In the FSC quintessence model, this scalar relationship holds true and is equivalent to 2 3 t R Λ = [16]. In FSC, the vacuum energy density declines in the forward time direction approximately 121 logs of 10 from the Planck scale epoch to the present. Thus, in contrast to ΛCDM cosmology, there is no "cosmological constant problem" in the FSC model.
As speculated in the FSC book chapter summary, ongoing cosmological matter creation may be paired with a continual decline in the cosmological vacuum energy density, as a requirement for conservation of energy in such a finite isolated expanding system. It should be remembered that the details of matter creation in all cosmological models are a mystery. In FSC, matter creation is an ongoing process, whereas ΛCDM cosmologists generally assume that all matter was created nearly instantaneously. However, as a result, a major difference between the two models is that only ΛCDM cosmology has a cosmological constant problem, based upon its embedded constant post-inflationary vacuum energy density assumption. When one compares the relative luminosity and angular diameter distances between the two competing models, in the form of a ratio, it has recently been shown that the ΛCDM model contention of late cosmic acceleration could be an illusion produced by a R h = ct universe [17].
Further support that cosmic acceleration could be an illusion is clearly evident in Figure 1 of the current report. It is readily apparent that the FSC graph of the log of the Hubble parameter as a function of redshift z is sinuous in appearance. We see The upward curving portion of our Figure 1 graph out to a z value of about 1.5, is already largely filled in by the accumulated Type Ia supernovae data [18].
Not yet known are the exact Hubble parameter values at the cosmic times when these supernovae exploded. Fortunately, the coming decade of observational studies should give us a better idea of the precise scalar nature of the Hubble parameter.
Regardless, given the overall shape of our Figure 1 graph, it may well be that apparent early cosmic deceleration and late cosmic acceleration both ultimately prove to be illusions produced by a constant-velocity, linearly-expanding, FSC universe.

Dedications and Acknowledgements
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