Dark Energy, Schmark Energy

Extraordinary claims require extraordinary proof 

DARK ENERGY, SCHMARK ENERGY 

There is no excuse for the current mad rush to a messy consensus and the cockeyed conclusion that some weird stuff some call dark energy makes up the bulk of the universe. Dark energy is truly miraculous and qualifies as a supernatural explanation of deep space observations! 

Since there is no experiment that could confirm or deny the existence of dark energy, it cannot be considered as a contender. Extraordinary proof is out of the question but, it is among the most extraordinary claims ever made. Its disqualification as a viable hypothesis under the rubric of the Scientific Method means that we must start from scratch.  

Those with the ability must recalculate the main assumption that underlies the dark energy hypothesis. Let the theoretical chips tumble where they may and the intellectual trees drop where they will. 

This dark energy hypothesis is designed to explain just one observation that is currently looked upon from the so called "weird science" perspective. This particular peek at reality is from a point of view that is based on just one interpretation of the real distances to type 1a supernovae. They are now interpreted to be farther away than their redshifts would indicate. But, an estimate of the most serious interference to this interpretation, that there may be much more or much less "grey" dust in the early universe than was initially thought, must be in error. 

This currently calculated observational result and theoretic premise is that there was not enough extra dust to cause the redshift effect.  But, the effect itself is a result of an interpretation that may itself also be wrong. 

This apparent "phenomenon" is that since these exceedingly distant supernovae are farther away than the distances indicated by their redshifts, then the universe "must" have begun expanding at an accelerating rate in recent epochs. The only thing that we seem able to think of that might explain this strange interpretation is this unscientific postulate of dark energy.

 

For various reasons, all subsequent observational interpretations may well have been biased to favor the assumption of dark energy to begin with, so it may not be too surprising that they do indeed tend to prove it. 

There has been no effort to go back and reinterpret "grey dust" observations nor to recalculate the relative theoretic prevalence of "metals" in the earliest phases of the universe's development. If mathematical assumptions are changed sufficiently, the concentration of heavier nuclei could easily rise to the point that more dust formed than is now thought. Presto! There was much more dust present to dim the images and the supernovae in question are as nearby as their redshifts indicate. The manner in which the assumptions must be jiggered may well lead to a bigger paradigm shift, a more profound revolution, than dark energy itself. If weird science is for what governments will pay, a bonanza is waiting to be won. 

Furthermore, gravitational redshifts have been totally neglected. Relativistic redshift is distinct and is applied to the data. But, the young universe was very much more dense and its much more intense gravitational field would have influenced any light traveling on a trajectory that would tend to have it escape - that would have it end up in our eyes. 

Why there is not much more skepticism about the contradiction between luminosity distances and redshift distances in the first place completely escapes me! 

Still, some critics of dark energy do not seem to have a clue. For instance, some confuse Doppler redshifts with relativistic redshifts. It makes a difference! 

Regarding those extremely distant type 1a supernova results, there is indeed much more to Relativity than relativistic redshifts. The gravitational field in the early universe must have been VERY much greater than it is now. So an additional Einsteinian gravitational redshift should be added to all light traveling on an "outward" or escape trajectory, that is, toward our eyes in space and time. But this is not done. If this correction was carefully applied, then the redshift data would be translated to the same coordinates as the dim supernova results and the discrepancy would disappear. 

Regardless, dark energy is not necessary. How then do we account for a very nearly flat universe if dark energy does not add to the total mass/energy inventory? 

Easy. 

The observable universe would be situated within a polydimensional surface or "brane" of an extraordinarily large black hole or something much like a black hole that may be in motion. Its total dimensionality could well be significantly higher than superstring/M-theory implies. There may be evidence of 11 dimensions in our universe because our very existence means that this, our cosmos, resamples the superdimensional volume of the interior of this theoretically invisible "Dark Pit" or "Dim Seed". 

Clearly, it would not be not black. Still, no matter falls out of its event horizon, the surface where events occur, where things happen. No matter disappears into it, so, it does not generate a whole spectrum of radiation on the way in. The Dark Pit would be completely beneath visibility. But, we may deduce its presence and, perhaps, devise tests for the hypothesis of its existence.  

If we cannot do this, then it is a nonstarter and the idea must be rejected, in strictest accordance with the scientific method. 

The mass of the Dim Seed or Dark Pit would be many times the total estimated mass of the observable universe, whatever may be required to make up for the total energy/mass deficit. The curvature of its surface would be very nearly flat, as theory and observation require, but not exactly flat. The tiniest variations from flatness, though they may show up within the error tolerances of measurements, could be real, in other words.  

In order to make its surface flat enough without exceeding the mass limit implied by the matter/energy shortfall, it would be spinning very fast. Residual anisotropy that has in fact been discovered that is not accounted for by our laboratorys' proper motion through the cosmos could be due to this rotation. This means that our universe would be spinning too, of course, and not necessarily at the very same rate or direction. By analogy, the spin rates of the sun are nonuniform. Precise measurements of the residual cosmic anisotropy (RCA) could nail down the probable spin rates. This idea may also have implications pointing to the real nature of mass and of matter itself. 

There may not have been a Big Bang either, this may imply. If this Dark Seed's dimensionality could include several orthogonal dimensions of time, its shape might still be like a flattened sphere or nearly flat pancake, but what is regarded as expansion of our universe, even acceleration of expansion, may just be due to its turbulent rotation in time. With a correct more detailed model, the properties of the Cosmic Microwave Background might be accurately predicted. Then the cyclic model of cosmogony may still make more sense. 

The idea of multiple dimensions in time is not such an outlandish proposal. All spatial dimensions may just as well be described as time dimensions because of the limit on the speed of light. The word "spacetime" means equivalence between space and time just as surely as E=mc^2 means equivalence between matter and energy. In certain cases like this, it may be more enlightening to think of certain dimensions in terms of a time reference instead of a distance or length definition. 

The Wiz's Dark "Horse Matter" is another even deeper and weightier mass of a different kind (and of a different color, of course). We all seem to like Alan Guth's inflationary universe scenario but we also seem to be unwilling to carry the implication of his ideas to their logical end. He postulates that the universe began as a quantum virtual particle that sprang into existence in an extremely high energy state largely because the whole field of spacetime was excited. It was a "false vacuum".  This quantum spacetime just naturally existed in such a very high energy excited state because, statistically, this is the most probable initial condition.

We cannot ignore the statistical nature of quantum mechanics here either. Analytically, not only must there be an antiparticle "out there" somewhere, the particle/antiparticle pair must generate interference particles, +/- and -/+. Statistically, they must be just as real as terra firma itself. For, as we all know, repeated observation, even of the surface of the Earth, gives only a statistical result. I can interpret what I see only because I have seen images like it several times before. I can regard a blue streak in the image as a river only because I have seen rivers up close and have even swum in them. If I compare my preceptions with those reported by others, the picture gains another layer of statistical importance. We gain a consenus only statistically.  

Furthermore, since we imply by this line of thinking that there is a reality outside this universe, there must be particles naught- and naught+,  -naught and +naught, representing the zeroth, or "nonexistent" states. Such entities may be nonexistent only from the perspective of a certain aspect of the meta-cosmos of which ours may be merely a subuniverse.  

They would all have mass. They should still be "close" enough for their gravitational influence to be felt within our particular version of this ultraverse. If a count is made of the possible quantum states that this scenario implies, the inferred energy/mass inventory, as a percentage, comes out just right. 

All this can be easily expressed algebraically. I have a discourse on the quantum operator algebra of this concept that shows that it is rigorously logical. I will furnish a copy on request.

Or else - to say the same thing, actually - the Many Worlds "multiverse" hypothesis may be true. But the number of interference and mixed existence states may be much larger than what I may imply above. The gravitational influence of Many Worlds would be felt within galaxies that rotate faster than we think they should. Either of these two approaches lead to the conclusion that we observe only a small fraction of the matter that is really there. That is, unless we do careful rotation rate studies on as many galaxies as we can. 

I am sure this has all been thought of before, but it bears repeating, especially because it solves problems that we never anticipated that it would. For instance, it answers the question of why there is not any antimatter in our universe. Well, there is, except that all we can see of one is its contribution to gravitational effects on the rotation rates of most spiral galaxies. 

And, it gives us a solid mechanism to explain those amazing galactic rotation rate profiles explicit in observations. These fit the concise mathematical treatment of the MOND effect (MOdified Newtonian Dynamics). Moreover, this mechanism does the job while preserving relativity.  

If deep space observations constitute quantum statistical effects, such observations must include an aspect of Heisenberg uncertainty. The unseen Multi-Quantum or Many Worlds phantom galaxies would not all rotate on the same axis nor in exactly the same positions nor orientations. Surely, a simple, straightforward statistical distribution of directions, rates and orientations could be found that precisley duplicates the MOND phenomenon. A distribution of  such distributions would enable hypotheses that explain just exactly why some galaxies fail to show the effect. So, the exceptions would prove the rule, perhaps. 

Remember, this discussion refers to both dark energy and dark matter. Reference is made to an hypothetical Dark Pit and to a quantum multiverse.  They must be aspects of the same entity. But, I have finally run out of words to describe it! Surely, if these ideas have any merit, superstring theory will have something to say about it. Can superstring theory handle a mere brane with 11 dimensions? Is this theory scalable? Am I talking about the inneffable M-theory?  

Returning to reality, why neglect easy solutions like this in favor of complex and difficult ad hoc postulates that raise more questions than they solve? 

In future posts I will explore this and present my most favored model for the inflationary expansion of the universe. It shows how the data should properly be interpreted. 

The main thing, though, is that dark energy is unnecessary. 

 

Black Hole Singularities and the Possibility of Two Dimensional Gravity

According to general relativity, in a 3-D universe with time, the gravitational field of all compact objects behaves as if the objects are point masses and the field strength must decline as 1/r². In a 3-D universe, therefore it is said, it is impossible to support a hyperbolic 1/r gravitational field. But, black holes are different.

 
Why bother with the whole concept of black holes if they are not different? Collapse of matter into a black hole must not only create a singularity (within the limits imposed by the Heisenberg uncertainty principle) but, the spin rate or orbital frequency of in-falling matter of the black hole must also increase without bound as radius r decreases to values near zero below the event horizon. Attempts to explain away these singularities on the basis of a non-existent quantum gravity scheme are vacuous extrapolations of tentative hypotheses that amount to pure conjecture.

 
Black hole singularities exist. Einstein through Schwarzchild and others say so. Who claims to be more brilliant than these fellows? I appeal to authority here only because it seems to be the only thing that impresses some. If you want to claim that BH singularities are mere artifacts of an inadequate theory, show me the Math.

 
Black holes are different. When matter and energy collapse under an infinitely strong gravitational field to a point mass that is as tiny as may be necessary to explain its properties (not necessarily to zero, the true meaning of infinity), the result is a phase change. Spacetime phase changes are S.O.P. in the repertoire of theoretical cosmologists, like Alan Guth. Let us adhere to the hydrodynamics metaphor used by Einstein in his development of GR. Flat spacetime is a massless superfluid. Helium IV is a superfluid but, it is not massless.

 
To extend the metaphor, it is not hard to imagine that spacetime could undergo a phase change, just as helium IV may. In a black hole this change involves a reduction in dimensionality. This is about the only change available to it. Analysis of the equations of GR shows that gravitational strength, F_g is proportional to 1/r^(n-1) where n = number of spatial dimensions. In a 3-D universe, F_g declines as 1/r². In a 2-D universe, F_g declines as 1/r.

 
So, a black hole must use the gravitational energy of in-falling matter to raise its gravitational potential, the gravitational energy level, to the 2-D “state”. We are starting to talk quantum language now.

 
The shape of this singular BH gravitational field strength diagram, as it is a 2-D entity embedded in a 3-D space, is a nominally flat disk or platter with a potentially infinite radius. Unlike Kerr, I call this topology of the event horizon a “spin disk” because it arises from the infinite rotational and orbital spin rate of matter that has in-fallen toward the singularity. As a spacetime entity, this new phase ignores the event horizon and propagates outward to beyond the edge of the galaxy. It emanates from the central core of the galaxy wherein resides any central supermassive black hole.



Here is one of the non-intuitive consequences of GR. It is known that matter in-falling toward the event horizon must experience time dilation. From our external perspective, we would perceive time for this matter as having slowed and even stopped at the event horizon. Viewed from any point outside the event horizon, time really does stop there. But from its own perspective time does not stop and such matter does indeed drop through the event horizon where it may take part in whatever processes it might (time reversed or not).


There is simultaneously an inverse square gravitational field set up by this time-frozen matter at the event horizon and an inverse gravitational field set up by this same matter that has already in-fallen to the singularity. There is no violation of conservation laws here because no object can feel these separate effects simultaneously. If an object orbits the galactic center in the plane of the galactic disk, it feels the inverse 1/r field. If it orbits on a trajectory not aligned with the galactic plane, if it orbits chaotically, it feels the inverse square 1/r² field.


This has consequences for the analysis of the orbital motion of close-in Milky Way bulge stars like S2 for the determination of the MW’s supermassive black hole mass according to Kepler’s laws. Kepler is valid for the 2-D case as well as for the 3-D case. But, it has to be adjusted for the 1/r gravitational field as does Newton’s law. No deep relativistic calculations are needed. One can determine what changes must be made in Newton’s law and Kepler’s laws by inspection.


Above, I explained how a 2-D gravitational field can exist in our 3-D universe. It must be associated with a black hole having an infinite spin rate as well as infinite density and infinite gravitational field strength. Within the bounds of Heisenberg uncertainty, these singularities must exist. There is no point in trying to explain them away using some kind of unfalsifiable overly advanced unintelligible gravitational quantum sophistry.

 
I show that the hyperbolic 1/r inverse gravitational field can exist as a spin disk surrounding any black hole with said disk extending far beyond the event horizon toward infinite radius. This explains MOND and the anomalous velocity dispersion because hyperbolic 1/r gravity means that orbital velocity, v, around a galactic center containing a black hole, v = (GM_bh)^1/2. That is, v becomes constant dependent only on M_bh and G. This v is not only constant for a given galaxy, it is constant from galaxy to galaxy. This means that GM_bh must itself be a constant, a new fundamental physical constant.


But, G may not be the same G that applies in 3 dimensions. So, I call it G*. Besides by an extension of GR, one might get G* from the M‑sigma relation as well as by the anomalous velocity dispersion. But, the mass of the central galactic supermassive black holes must first be refigured on the basis of the hyperbolic field if very many of the orbits of the bulge stars that were used to get M_bh were coincident with the galactic plane. If all or most of these orbits were chaotic and not aligned with the galactic plane, the BH mass determinations may be okay.


The new fundamental physical constant should actually be written G*M_bh such that G* and M_bh are not independently variable but together form this constant that I call Ḡ. Ḡ is constant only under the influence of the gravitational field of a given black hole.

 
The meaning of the hyperbolic gravitational field of black holes is that MOND (Modified Newtonian Dynamics, suggested by Mordehai Milgrom) is explained without recourse to Dark Matter or to modifications of Newtonian dynamics. Newton and Kepler must be understood in two dimensions, that is all.

 
All of the observations that are said to support Dark Matter as being, say, a huge halo of WIMPs engulfing galaxies and galactic clusters also support the hyperbolic (1/r) gravitational field postulate, even the Bullet Cluster effect.  Dark Matter 3-D maps obtained by analysis of gravitational lensing also follow logically from the Postulate.

The hyperbolic (1/r) supermassive black hole gravitational field is indeed a postulate. This means that there can be no argument against it. It must be taken at face value and carried to its logical extreme whereupon it will be either reduced to absurdity or else found to be correct.

 
When extrapolated to the entire universe, the hyperbolic field mimics Dark Energy too. If Alan Guth’s inflaton particle originated in 2-D space and began to roll down its own hyper-gravitational super-potential slope toward a lower energy 3-D state, the higher energy 2-D potential energy would be progressively transformed in a time dependent quantum-like transition to the new 3-D “ground state”. This potential energy would show up as apparently increasing kinematic momentum of all stars and galaxies in the universe. That is, the universe would appear to be expanding at an accelerating rate.

 
This is an exciting idea because the whole universe is thus to be regarded as a quantum object. It may provide a route to a falsifiable certifiable theory of quantum gravity because 2-D gravity does not lead to a gravitational catastrophe as r tends to 0, and it is renormalizable, a prerequisite for any quantum theory of gravity. This Postulate may point to a means to prove the existence of the multiverse. If Guth is right, Hugh Everett could be right.

 

 

Dear American Gypsie

In reply to AmericanGypsie for the comment given several posts ago:

Grey dust has been eliminated by the observation of the magnitude/redshift relation for very distant SNe Ia supernovae. Their spectra, brightness and redshifts are all concordant with calculated great distances.

Interstellar gas will not cause redshifts unless it is ionized, like a plasma. But, the existence of a plasma would eminate from all distances so that the distribution of locations of plasma emmision sources would not match the observed emmision source locations. And, the CMB power law (a type of frequency distribution) across the sky and across the spectrum, would not match the observed CMB (you know, that pretty sky chart showing the red and blue patches got from the WMAP satellite).

The disparity between the radius, radius of curvature or Hubble radius derived from H naught and the the magnitude of the scale factor got from application of the Friedmann equations is very large. This lack of agreement stems from the fact that the Friedmann equations calculate the scale factor of the entire universe, not just the "observable" universe.

The inverse of H naught gives the Hubble radius or the approximate size of the observable universe (U). There are other ways to calculate this dimension depending on the type of observation that is made. But, they are in good agreement. For instance, the size of U is a bit smaller because the value of H naught that is obtained for X-rays by the Chandra X-Ray Observatory is a bit larger (77 km/s/Mpc) than the value for H naught got from ancient SNe Ia (72 km/s/Mpc). Brightness measurements alone indicated the universe is very large and very old.

X-ray redshifts will be very different from microwave redshifts and would occur by different mechanisms if it was caused by interferences and not by virgin emmision from the the time of "recombination" after the Big Bang.

It's funny that you suggest scientists may be Christians in disguise. They are mostly atheists or agnostics.

The Plasma panacea that has been proposed to account for everything is being pushed by Fundamentalist Christians as indicating that U is much younger, say, about 6,000 years old. They want to debunk the Big Bang and all it entails because it indicates age in the billions of years.

They will never succeed and they should give up.

Your comments are very good and I appreciate the thought that you have obviously given to this issue. If only certain scientists would give it the same.

However, I surely would not call general or special relativity mere scientific popularism. The Principles of Relativity are the second best validated pillars of all science.

The first best validated Principles are those regarding quantum mechanics and particle physics' quantum chromodynamics (the God Particle type of a merger between quantum science and relativity).

Because popular books have been written does not mean that they have no serious basis just because they are popular.

Black-Hole Gravitational Field

The Hyperbolic

Black-Hole Field Anomaly

Supermassive black-holes pervade the universe. In the field of our view, within the light cone of our observational limit, there are over 200 billion supermassive black holes residing at the centers of large galaxies. There are probably many more large naked black holes residing in enormous dust clouds or simply standing alone as bald singularities in elliptical galaxies and globular clusters and within galactic clusters and superclusters. These invisible black-holes simply have not had enough time to accumulate a large cloak of glowing matter that emits light by virtue of its in-fall to their event horizons. Therefore, they are truly black.

Black-holes and their hyperbolic gravitational fields fully account for the dark matter necessary to keep galaxies spinning at their observed rates and to bind galactic clusters and superclusters. If there are large enough numbers of such black holes to do this job, then the assumption of the Cosmological Principle is dead wrong by this fact alone.

It is as though the universe is made of Swiss cheese and we have assumed it is made of white cheddar. It is well known that a medium filled with small bubbles or tiny solid particles behaves very differently toward the propagation of any type of energy through it. Numerous small bubbles, for instance, lower the speed of sound and affect the way a medium like water absorbs microwaves. Shock waves propagate so differently that the behavior of the explosion front in the conventional chemical explosive has to be taken into account in the design of nuclear weapons. Bubbles and dispersed solids must be avoided.

When assumptions are made regarding the type of "perfect fluid" of which the universe is made we cannot disregard exceptional circumstances like the presence of a froth of black-holes embedded within it. It matters little that there are good reasons for using approximations like the Cosmological Principle. Something must be done to allow the formulation of comprehensible theory giving the means for tractable calculation. But, this theory and such calculation must be regarded as only approximate. Unless steps are taken to greatly refine theory and bring calculations up to a much higher standard, there shall be no such thing as "precision cosmology".

The hyperbolic black-hole (HBH) gravitational fields, stemming from supermassive black-holes at the centers of galaxies, extend far beyond the visible boundaries of the galaxies themselves. The Modified Newtonian Dynamics (MOND) effect shows that these fields may be virtually infinite in extent. If this is so, the spacetime continuum that is actually present in the universe is very different from the one that Einstein assumed. These oversimplifications are implicit in the Friedmann LeMaitre Robertson Walker metric that Friedmann used to formulate the form of the General Relativity equations that cosmologists commonly use. In other words, the whole structure upon which is built the argument for acceleration of the rate of expansion of the universe and the existence of dark energy (not to mention dark matter) is deeply suspect.

It is just too bad, so sad, that so many physicists have devoted whole careers to mastering the mathematics of General Relativity from the perspective of the FLRW metric and the Friedmann equations. These anachronistic personalities will simply have to die off or retire before we can make progress. After all, there is some truth in the saying about physicists who see everything in terms of some simplifying assumption. "First, we assume a perfect sphere." is not how to do critical science deserving of massive funding.

Only spacetime itself is homogeneous and isotropic. But, once it becomes filled with supermassive black-holes and other dark naked singularities, it cannot be treated this way with any degree of precision or accuracy. Some investigators have already picked up on this fact. They are formulating new cosmologies with different metrics and are abandoning the oversimplified assumptions that were designed to make calculations easy. Much too easy. They have come to appreciate the power of supercomputers and advanced mathematical logic programs to handle more realistic models of the universe. This twenty-first century trend is only just beginning. The real revolution in cosmology has yet to come. It will be a counterrevolution, for the twentieth century is dead.
　
　
　

INEXPLICABLE REVISIONISM

Some of Our Best Scientists

Have Shown Genius Level Negative IQs

Recently there has been an inexplicable reversal in the usual recitation of facts that scientists have been giving regarding the evidence for dark energy. Here is a quote from a current article on dark energy and dark matter that appears on a NASA website: "Then came 1998 and the Hubble Space Telescope (HST) observations of very distant supernovae that showed that, a long time ago, the Universe was actually expanding more slowly than it is today."

This is grossly untrue. If this is what Saul Perlmutter and Adam Riess have been saying, it is a gross distortion. In them, I am disappointed almost to tears. But, what else can I expect from the antigeniuses among us?

I have been tracking measurements of the Hubble constant for many years. The Hubble Space Telescope has measured H0 for the deep space SNe 1a as the highest yet recorded except for H0 determined for the cosmic microwave background radiation, which is even more "distant" and even older. As one plots H0 measurements against the average distances from Earth to the midpoints of the ranges of objects used in the observations, one obtains a very precise straight line in this scatter diagram. This linear regression line has a very high correlation coefficient (0.98) and a NEGATIVE slope stretching from the origin at t = 0 to now at t = 1.

Given that H0 is not really a constant, older accepted data along with current measurements of H0 show that H0 for very distant and old objects is larger than for nearer and younger objects. Nowhere in any of the peer reviewed publications of Perlmutter nor Riess is there explicit argument for acceleration or dark energy that does not subtly assume what it purports to prove. They never explain exactly how the reversal of common sense occurs that says the universe expansion rate is accelerating in the present era. They do not even acknowledge the reversal.

Commonly accepted facts have to be rewritten to accommodate this circular conclusion. History has to be revised. Accepted data clearly show that the expansion rate is decelerating. See http://www.lonetree-pictures.net/Graphical%20Model%20of%20the%20Universe.htm .

There is lots of evidence against dark energy. Recent papers casting doubt on the Cosmological Principle should be taken seriously. If we should be prepared to accept the many patches and ad hoc band-aids that dark energy requires, why can we not entertain some patches to explain away the so called "evidence" for it and help save the Scientific Method?

One does not validate a scientific principle by accumulating circumstantial evidence. Such are just anecdotes. One must formulate an antithesis; an opposite or negative hypothesis, and attempt to perform a critical or crucial experiment that would confirm or deny it. If this “null hypothesis” is confirmed, the original hypothesis is falsified or nullified. Dark energy is incapable of falsification and is thus as ineligible as a scientific hypothesis as Santa Claus or God Himself. To hold otherwise is to open the gate to superstition.

The Model - Inflationary Expansion of the Universe, Tables of Equations and Variables

"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

New Empirical Numeric Model of the Evolution of the Universe

Phenomenological Mathematical Model of the Universe

I think that once galaxies have begun to form, the origin of the universe was quite done and its fate was sealed. Undoubtedly, there will be more progress in the physicodynamics of galaxy formation. Once discrete large scale structures begin to form in the universe, the assumption of the cosmological principle that the universe is homogeneous and isotropic begins to break down. But, before this time, it was probably perfectly appropriate.

I have never seen a mathematical model of the "origin" of the universe and its evolution, growth and development carried through to the present era and beyond. Such a model has been inferred from the data, but I don't think it has been explicitly expressed in analytic mathematical terms. Using Guth's inflationary scenario, specifically his premise of an exponential burst of growth near the very beginning, I have developed a mathematical model that is capable of depicting the evolution of the universe from 10 ^ -60 sec to 30 gigayears and beyond.

By using various choices for parameter values, it is possible with this model to represent a universe that putatively follows a trajectory true to empirical data and transitions to a new era of "neo-inflation" or dominance by dark energy. Or, it can move toward a period of deflation toward collapse in the modern epoch. Or else, it may evolve toward "flat" expansion at a constant rate. Adjustable parameters make it possible for my model to mimic any empirically determined behavior with but very few input values. The plots that I can produce may have significance beyond their graphic utility for visualization.

I use Einstein's natural units to represent the "radius" or radius of curvature of the universe, time and the speed of light. This is the only way that Guth-like equations make any sense and are definable. A plot of these equations, their 1st and 2nd derivatives, H and the expansion of the universe if it had expanded at the speed of light, seems to show a sort of symmetry.

The existence and positions of multiple intersection points where these curves cross in interesting ways portrays an array that might be interpreted as a representation of several kinds of invariance. I am tempted to interpret this array of intersections as a highly symmetric matrix of invariances, also invariant and symmetric in their superimposable, rotational and other transforms of coordinate systems, bespeaking various fundamental constants according to Noether's Theorem.

Revealed here is an interesting problem. I refer to my equations as empirical or phenomenological models that are based fundamentally on theory so that it should be possible to extrapolate successfully into the past and future alike. Using parameters that give a result consistent with the onset of a new epoch of inflation in "recent" times, this form of the model does not provide an early time when the nascent universe could have equilibrated.

Essentially, Guth's idea fixed the major criticisms of the Big Bang Theory by postulating that equilibration occurred during the exponential induction period when the universe was very small and that the transition to exponential growth then locked in the homogeneity that had been achieved. But, with the choice of parametric values giving the required result of that new inflation attributed to dark energy, there is no such induction period.

And, because there are fewer multiple intersection points displayed by this type of plot, it displays less of the above described symmetry than a plot of a type that displays developmental deceleration. Plots showing deceleration show higher "symmetry" and they provide a type of induction period in the traces of their curves. Mathematical physicists prefer theories that possess more of this kind of symmetry.

I want to combine the two types of equations by merely adding them together with variable weighting factors as is done with hybrid solutions to a quantum wave equation. The weights might themselves follow a simple equation that emphasizes the deceleration scenario in the first few moments of the universe's existence and the acceleration scenario later in its evolutionary trajectory. Then, the early induction period would be preserved while the transition to new inflation would be allowed. I want to see if my special symmetry is preserved and see what my being able to do this might imply. I will expand upon this in a future post that will be entitled "The Quantum Universe".

Of course, if the universe really did originate with a singularity, no induction period would be required. Guth's inflation might not be needed after all. If the trajectories of all waves and particles originated at the same point, they would progress throughout the whole with at least some of the same "original" intensive properties, like temperature.

The Big Bang, the origin of the universe, was not an explosion. If space-time expanded from a single point, it is unnecessary to postulate any form of unevenness or turbulence that might give rise to inhomogeneities that would need to be suppressed or quenched. Precisely what cause could be cited that would result in an uneven expansion of space-time or a turbulent beginning with consequent temperature variations? Are not temperature variations simply assumed? Why? The failure of the explosion metaphor must have a consequence.

Gary Kent

Dark Energy Debunked Still More

Re: Dark Energy Debunked

O.K. Suppose the expansion of the universe is accelerating against all previous hypotheses that it should be decelerating. How could it be?

Well, Dark Energy is one explanation. Dark Energy is supposed to act, physically and mathematically, like negative pressure. It is as if the universe was immersed in a big vacuum, except that it is already a vacuum. But, it may be what is called a "false vacuum" with many more quantum entities seething just below the level of detectability (without huge accelerators probing muon decay, that is).

The true vacuum would act on our false vacuum universe the same way that a vacuum would act on a balloon, and, as the membrane got thinner, it would weaken. This is because the tension or overall force had surpassed the elastic limit and the expansion rate of the balloon would therefore accelerate. The tension seems to have surpassed the elastic limit of our universe about 9 billion years ago, it is said.

But this is just analogy. It is meaningless if it does not lead to a testable result or deduction. We cannot apply a force to the universe as a whole nor to spacetime. We cannot stretch spacetime in an experimental apparatus.

Perhaps spacetime stretches naturally as a result of the expansion that has already gone before. Then, as the receding galaxies recede faster from one another depending on their distance, it constitutes increased stretching of spacetime. As a matter of fact, the relativistic redshift is said to result from a "stretching" of spacetime.

But, I am only restating my analogy in different words (dodging or begging the question). This is not experimental or observational proof.

We need to put spactime in a sort of tensiometer to stretch it until it deforms more rapidly or else breaks. We need to find a way to rip spacetime. And hope that we do not tear a hole in the universe that will swallow us up!

This is all unproductive speculation. It would be more productive to follow the lead that this Dark Energy conclusion, reached by reductio ad absurdum, has given us. Carrying an argument to its extreme this way, to the point where an absurd contradiction occurs, is a standard method of proving logical falsehood.

Dark Energy proves itself false.

Let's work on this!

Then the calculations that indicate that the theoretic prevalence of heavier nuclei in the early universe are wrong, and the premises leading to this conclusion of too few heavy nuclei, need to be revised. Furthermore, the premises behind the interpretations of observations of too little "grey dust" that is made of such heavy nuclei (Be, B, C, N and O with traces of Mg, Al and Si) must also be wrong. There is a goldmine of research opportunity here!

Yes, scientists have made an 180 on the deceleration/acceleration trajectory of their thinking. And, yes, there could indeed be 1,000 million big bangs and other even weirder local parcels in a truly infinite universe. So, what is so special about it, even if our packet of the universe's expansion rate is accelerating. Who gives a rat's ass?

Well, we do, because we are here. And we do indeed live in a universe that just happens to have physical constants that support its existence and the existence of intelligent life. Presuming that we are indeed intelligent, that is. So, it matters to us because such conundrums fascinate. The irony is irresistible.

Another explanation of accelerating expansion is that spacetime is exploding. The negative pressure that shows up in relativistical equations is itself only relative. From the outside, looking in - even with an explosion - the pressure is negative. Just as energy is negative if it is released from the inside to the outside. The result is the same as before.

Except it is more like the original "phase change" that the "false vacuum" underwent at the time of the Big Bang. When water begins to boil, the expanding bubble drinks in more vapor at an accelerating rate because its surface area is increasing so rapidly that it ensnares more and more liquid, allowing it to turn into vapor. The false vacuum returns to its ground state, the true vacuum state, releasing energy that goes to accelerate the expansion rate. The bubble of spacetime that is our universe increases in size at an exponentially increasing rate, like a bubble of steam that grows larger so fast that it almost explodes out of the tea kettle.

These two scenarios are called the "quintessence" hypothesis and the "cosmological constant" hypothesis, respectively. Not only do we have to prove Dark Energy exists, but we have to distinguish between these two alternatives!

It would be much simpler to suppose that the premises underlying theoretical calculations and observational interpretations about the disparity between luminosity distances and redshift distances to far off type 1a supernovae are wrong.

Another alternative would be that the universe is growing. Spacetime may be reproducing itself and it is doing so at the usual exponentially increasing rate typical of a population of living organisms. The spacetime population underwent an initial accelerating increase initially (the BB), slowed down when waste products (like neutrinos) accumulated and sped up again when the volume increased sufficiently (and neutrino density decreased enough) for a new growth spurt to begin. Perhaps the conclusion should be, from this if it is true, that the universe is alive!

Gary Kent