Dark Energy, Dark Matter, Quintessence, Cosmological Constant

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George LeMaitre suggested that the universe should be expanding at a steady rate in the present time, and has been doing so for eons. Edwin Hubble discovered that the universe is indeed expanding at a rate that he determined and this rate has been called "the Hubble Constant".

It is now well established that the universe is expanding, but not at a constant rate. I believe that the universe's expansion is slowing down, or decelerating. Other scientists think it is accelerating.

My equations or the MODEL that I have developed, suggests that deceleration is the only way to explain all the facts and that acceleration, the model favored by many cosmologists, is not such a good account of reality.

Acceleration is concluded from a particular interpretation of some observations. It is not necessary to choose this interpretation.

In order to explain this acceleration, ad hoc postulates have been offered. These kinds of off-the-cuff explanations do not explain anything. They complicate matters instead. One of the complications this causes is that there must be some sort of "Dark Energy". DE might stem from Einstein's cosmological constant which he slap-dashedly stuffed into his theory of relativity.

DE is supposed to pervade the universe and is forcing it to expand at an ever increasing rate. Then, if there is such a thing, the total mass & energy inventory of the universe must be so much larger than was thought that this surprise has to be explained too. The trail of ad hoc postulates gets longer and longer as more band-aids are applied to a wound in the logic of the acceleration model.

Very recently it was found that the evolutionary development of galaxy clusters and superclusters is slowing down. This would be expected if the develoment of the whole universe is slowing down (decelerating). But, in order to keep the acceleration idea alive in the face of this fact, more band-aids are needed. More ad hoc fixes are required to make sense of this galactic cluster develpment retardation effect.

It's crazy.

There is no Dark Energy, never was and never will be.

"radius_1" Depiction, Acceleration Scenario, multiple plots

RADIUS_1 DEPICTION

The next figure in the following post describes the case wherein the universe is expanding at an accelerating rate in the present era. Note that the Hubble parameter curve does not intersect t=1 at a reasonable point and that there are few points of multiple intersection.

By the way, the equations for the derivative curves were found by using the Mathematica website that features a free utility that finds derivatives. Of course, the first derivative represents the speed of expansion and the second derivative stands for the acceleration or deceleration.

Graphically, this scenario displays less symmetry and does not much illustrate Noether's theorem. Remember, these equations are semi-theoretical as well as based on phenomenology. So, being theoretical in part, they should be potentially able to respect Noether's theorem.

"radius_1c", Radius vs Time, Acceleration Scenario

"Radius 1c", Depiction of the Derivative of Exponential Deceleration

DEPICTION OF THE DERIVATIVE OF EXPONENTIAL DECELERATION

In the next post, I give the last figure. There, the plot represents the result of taking the first derivative of the exponential expansion equation that shows deceleration in the modern epoch. Looking at a short interval of time very near the beginning, we see that the speed of expansion runs through a minimum.

This may be important because these exponential curves show no induction period which is essential to serve their purpose of providing an early time for equilibration of the universe resulting in the eventual thermal homogeneity that we see now. The speed of expansion temporarily drops far below the speed of light, almost to zero, to give a minimum at a very early time. The case wherein the expansion accelerates in the modern era does not display this minimum. So, this is another reason to favor the deceleration scenario if one requires a time in the early history of the universe when equilibration could occur.

I wonder why the equilibration requirement is present in the first place. The Big Bang was not an explosion. It was a sudden expansion of space-time. There was not necessarily any turbulence to act as a source of inhomogeneity that would need to be smoothed out. Indeed, if the universe did in fact originate in a singularity, expansion from a single point should automatically result in a universe that is homogeneous and isotropic, satisfying the cosmological principle. To suppose otherwise requires a mechanism to produce turbulent expansion and none is forthcoming.

So, in order to favor the deceleration scenario, one would need to explain the supernova 1a results that indicate that the universe may be undergoing accelerating expansion in the present epoch. I would say that perhaps these results are a sort of optical illusion stemming from the possibility that when the universe is observed at such early times, it is observed as a more and more purely relativistic object. The tiny residual positive curvature of space-time may become sufficient to produce a kind of distortion of our measurements. Our gross difference in perspective results in what naively looks as if the universe is expanding at an accelerating rate. In other words, acceleration is an artifact.

The apparent development of galaxy clusters being slower in the very early universe than they are in the more recent epoch can be explained in similar fashion in that this is an artifact; this time, of the universe being very young. Youth, per se, must have some consequence, after all.

All plots herein were produced using the mathematical analysis program TK Solver Plus 5.0 by UTS.

Figure 2, Radius vs Time, radius_1c