Curvity, Dark Energy, Dark Matter and Modified Newtonian Dynamics (MOND)

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Dark Energy

One mystery that current physics has difficultly explaining are the results of a 1998 study by two teams who used "standard candles" called type 1a supernova to measure the expansion rate of the universe. The teams independently found that not only is the universe expanding, but it is doing so at an accelerating rate. "We had been working on using supernovas to measure the expansion of the universe, and about five years ago found that the universe was not slowing down, was not just coasting along, but has been speeding up, accelerating," says Robert Kirshner, an Astrophysicst at the Harvard-Smithsonian Center for Astrophysics and a member of one of the supernova teams.[1] It was a result completely at odds with what was expected from a universe supposedly ruled by attractive or "positive" gravity because the expansion should have been slowing down at best or expanding at a constant rate at worst. But for the expansion to accelerate meant that something was pushing the galaxies apart, not pulling them together as gravity should do. That pushing force has since been called Dark Energy.

With the problem of Dark Energy firmly in our minds, let's reread an important part of Daniel's story:

"A number of interesting but hardly convincing theories have been advanced in the attempt to reconcile the observed state of the Universe with the existing concept of universal attraction. Some of your cosmic theorists have proposed that at one time all of the matter in the Universe was contained in a single tremendous star or 'atom'. For some reason, which is not given, this atom exploded hurling outward the matter, which has become the star clusters and imparting to them the motion which we now observe several billions of years later. I shall discuss this theory further later on and will only point out here that such a theory will not stand up when examined under your linear concept of physical law."

"In first place, such an inconceivable huge mass of matter, even at a very great temperature which was assumed for it, would under Newtonian laws produce a gravitational field so intense that no velocity less than that of light itself would be an 'escape' velocity. In fact, it has been calculated that even the light emitted by this huge sun would not escape completely but would circle in a comparatively small orbit about it."

"Through the concept of the curvature of physical law, however we see that the addition of mass to an existing body does not, necessarily increase the force of attraction between its parts, but may, under certain conditions, cause the field to become negative and the attraction to become a repulsion. We can explain the observed actions of the present Universe by postulating that an attraction exists between the individual bodies within a galaxy because their total mass and distance is such that they are within the positive portion of the gravitation curve with respect to each other. In the vast spaces between the galaxies however, the curve dips below the zero line with the result that a repulsion exists between the galaxies themselves. This also explains why matter, although rather evenly distributed throughout the known Universe, is not distributed uniformly but is found in quite similar concentrations at comparatively regular distances."[2]

In regards to the formation of galaxies and their affects on one another, Daniel also wrote:

"We must, therefore, seek a spot which is remote from any of the existing galaxies, and approximately equidistant from the nearer ones. Even in this remote area of space we will find countless numbers of particles of matter, anti units of charge; electrons, protons or simple atoms, which have achieved escape velocity from some star, or which have been formed in space by random approach and capture. In short, we have all of the building blocks of nature, present in an exceedingly tenuous and diffuse state. Since each of the particles of matter has mass, each has a force of attraction existing between it and ever other particle of matter in the area.

If we accept the concept of the non linearity of natural law as previously outlined in this text, we find that each of these particles is also being repelled slightly by the surrounding galaxies or galactic clusters. These forces are almost inconceivably small, yet the net result of their action is to create a tendency upon the part of each randomly moving particle to move ever closer to the center of the area of attraction, which is also approximately but not exactly the center or 'null balance' point of the repulsion of the surrounding galaxies. We will assume that we have now reached the point from which we will observe the birth of our new galaxy. This point is at the center of a sphere of space, perhaps thirty thousand light years in diameter, within which the final concentration of matter will take place.

We must be prepared to exercise a great deal of patience, because the forces involved, and the resulting accelerations are so minute that many millions of years will probably elapse before we can detect any significant increase in the number of particles per unit of volume. Nevertheless, all of the particles within several hundreds of thousands of light years are slowly but surely acquiring a velocity in our direction. As the concentration of matter at the center of our system increases, the intensity of its field will also increase and will add, not only to the velocity, but also to the acceleration of the inward moving particles. We are observing the condensation of a tremendously large volume of exceedingly ratified gas into a relatively small volume.

Let us assume that one hundred million years have passed since we first occupied our point of observation at the center of the newly forming galaxy. All of the particles within some thousands of light years have now acquired a very respectable velocity in our direction, and the density of the gas surrounding us is increasing with comparative rapidity. We observe however, that the particles are not falling directly toward the central point of the condensation.

We can understand this if we realize that the center or null point of the force of repulsion is determined only by the distribution and the distance of the surrounding galaxies, while the center of the force of attraction is determined by the distribution of matter within the area of condensation. Since the center of 'push' is not at the same point as the center of 'pull', there is a tendency toward the creation of an angular velocity. That is: the particles, instead of falling directly toward the center, will tend to spiral inward. Eventually this rotational motion will become general throughout the mass."[3]

From Daniel's description of how galaxies form using negative gravity, we can explain Dark Energy. If you start from the center of a galaxy and travel far enough away, then gravity will not only drop to zero, but it will go negative. Anything outside the galaxy, including other galaxies, will be pushed away and that is how galaxies not only form as Curvity explains, but it can also explain why galaxies are all moving away from each other.

Curvity can explain Dark Energy by suggesting it is negative gravity, the result of both the mass of the surrounding galaxies and the distance from them. In other words, within galaxies, there is positive gravity but because the laws of physics are curved, gravity is negative between galaxies.

If negative gravity, as predicted by Curvity is correct, then we can make some predictions, for example, galaxies in dense clusters should have some sort of measurable effect on each other. Such an effect exists and it reveals itself as a relationship between the density of a galaxy cluster and the type of galaxies that are formed in those clusters. The relation is called the "morphology-density relation", first studied in depth by A. Dressler in the 1980s[4]. He found that elliptical galaxies were more prevalent in dense galaxy clusters than in "field" clusters where galaxies are spread apart. The opposite correlation for spiral galaxies exists where they dominate "field" clusters but are rarely found in dense galaxy clusters. The details of how Curvity can explain the morphology-density relation isn't clear, but it is encouraging that evidence exists that the proximity of galaxies can affect the type of galaxy that forms.

Existing science does have a few possible explanations for Dark Energy, one of which is the cosmological constant from Einstein's Relativity. The cosmological constant was Einstein's way of making the universe that he preferred, a constant one, neither expanding or contracting but existing in a steady state, using his gravitational field model in which the field is always attractive. However, in trying to use it to explain Dark Energy, it has serious flaws. For example, it doesn't propose a mechanism behind Dark Energy, nor does its calculated value predict the modern observations. Again, Robert P. Kirschner, explains the problem:

"Looking at Einstein's equations, it is easy to see that you get acceleration from a component of the universe that has positive energy and negative pressure. While the cosmological constant does that, it has some other properties that are distasteful to theorists. First, the measured value is so small compared to the theoretical estimates. They compute at least 1050. We measure 0.7. Second, the number measured for dark energy, 0.7 is not so different from 0.3, the value for dark matter. But that wasn't true in the past and it won't be true in the future if the dark energy is the cosmological constant. ... Why do we live at the unique and cosmically brief moment when they are about the same?"

"But most theorists are, quite rightly, suspicious about coincidences. They would be happier if dark energy were somehow related to the dark matter, so there would be a reason why they were so nearly the same."[5]

Dark Matter

Which brings up another problem for cosmology and that is Dark Matter. In the 1930s, an astrophysicist by the name of Fritz Zwicky realized that galaxies in the outer regions of galaxy clusters were moving more quickly then they should, based on the visible mass in the cluster. He calculated that there must be a lot more mass in the cluster if the outlying galaxies were not flying away from the cluster. In one galaxy called the "Coma Cluster" he found that up to 9/10th of the matter was not visible and he called it Dark Matter.

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Fig. 1

During the 1970s and 1980s, Vera Rubin, another astrophysicist, found that in a similar manner to Zwicky's clusters of galaxies, stars on the edge of galaxies were moving more quickly than the mass of the galaxies allowed. Similar to our own solar system, we would expect that those stars nearest the center would be moving the fastest and those stars at the outer edges would be moving the slowest. Just like Mercury takes only 88 days to take one complete orbit around the sun, and Pluto takes 248 years! The speed of rotation of stars about a galaxy's center, based on Newtonian physics, would look like a mountain which starts low, then rises to a peak and quickly falls off. But when astronomers measured the speeds with which stars orbited around the galaxy center, they found a surprise because the rotation speeds didn't fall off as expected, but stayed constant or "flat" as they got farther from the center of the galaxy.

To explain the unexpectedly constant rotation speeds, physicists have two choices, they can postulate a "halo" of as-yet undetected "dark matter" that only reveals itself through it's gravity or they can start fiddling with the law of gravity itself. By far the most popular option is the first and astronomers have looked hard for two types of matter, WIMPs and MACHOs. MACHO is short for "MaSsive Compact Halo Object" and is a play on the name of the other theory, WIMPs which stands for "Weakly Interacting Massive Particles".

MACHOs are large planets or small invisible stars which could only be detected by their gravitational influence, both of which would have to form in halos by the billions around galaxies to explain the Dark Matter problem. But there are big problems with the MACHO theory which can be summed up as "Where's the beef?". If there is a halo of Jupiter sized objects around our galaxy influencing the orbital speeds of our galaxy's stars, then there must be around five thousand billion of them which is a lot compared to the only 200 hundred billion stars. That is a lot rock but is it there? One of the first studies done with the Keck telescope when built in 1996, was to study extremely distant galaxies, which, because the light from them has been traveling a long time, is like looking at them when they were very young. What they found was that they contain a lot more deuterium then our galaxy does. Deuterium, or heavy hydrogen, is important because, using well-established calculations on star formation, they know that when there is more deuterium at the start of our universe, then there are less stars, planets and regular matter that can exist today. It is an inverse relationship because more deuterium at the start means less regular matter that can exist now. After measuring the amount of deuterium in the young galaxies, they realized that there was just enough to allow for what we see in the visible universe today, but way too much to allow all that rock that MACHO requires in the halos. The MACHO rock is missing!

That leaves the WIMP theory, but it has two major problems of it's own, the first is that nobody has detected a WIMP particle and secondly, even if they do exist, it isn't clear why the WIMP particle would prefer to exist in halos around galaxies.

MOND

What is exciting for Curvity is the possibility of the second option, fiddling with gravity itself. In the 1980s when Dark Matter landed on the door step of astrophysists like an unexpected baby, a theorist by the name of Mordehai Milgrom found a potentially correct baby formula. He came up with a theory called MOdified Newtonian Dynamics (wikipedia.org) or MOND which says that gravity at "very small accelerations", some 1011 times less then we feel on the surface of earth, falls off more slowly then Newtonian gravity predicts. If a galaxy was ruled by MOND, then as you travelled to the edge of a galaxy measuring gravity, it would drop off more slowly then you would expect using Newton's laws of gravitiation.

MOND can explain the "missing mass" problem without resorting to a sea of invisible, undetected particles (WIMPs). The reason MOND has gotten any attention at all is because when it is used to calculate the rotation curves of galaxies, it matches the measured results and has made a number of predictions that have since been validated by evidence. Compared to competing theories like Cold Dark Matter (CDM), MOND's predictions and confirmations really stand out, which is good news, because MOND can be explained by Curvity. Because both MOND and Curvity modify gravity at the extremes of distance and mass, then maybe there is a connection between the two. To reiterate, MOND says gravity, at the extremes, falls off more slowly then Newton predicts and Curvity says gravity, again at the extremes, falls off more quickly, hits zero and goes negative. As Daniel described, the negative gravity from one galaxy affects all the surrounding galaxies, even playing a part in their formation.

How Negative Gravity Contributions can result in MOND

We can postulate that the reason galaxy rotation curves are flat is because, as the positive gravity falls off, it is being compensated for by the negative gravity from surrounding galaxies, both of which accelerate the stars in the same direction, toward the center. The effect of both internal positive gravity pulling and external negative gravity pushing results in the same effect as if saying that gravity falls off more slowly then Newton's laws suggest. MOND modifies gravity by suggesting it drops off more slowly then predicted and Curvity can explain MOND by saying gravity drops off more slowly because negative gravity from surrounding galaxies push the stars toward the center. Curvity can explain the mechanism behind MOND.

Curvity also allows us to explain why some galaxies may have unexpected rotation curves (vs MOND) and it is because the surrounding galaxies are far enough away that their negative gravity contribution does not line up with the dropping gravity of the galaxy under study. Hence a galaxy rotation curve may not be flat, but have a slope, where if the surrounding galaxy(ies) are too far, the slope will drop, or if the galaxies are nearer, the slope will rise. The diagram to the right is a bit confusing because it isn't showing a rotation curve, but a measurement of gravity versus distance (and not an accurate one). The point is that if a negative gravity contribution from a surround galaxy is strong, the rotation curve will have a positive slope (bottom example). If the negative gravity contribution is not large, the rotation curve slope will be negative (pointed down in the top example). Remember, the red lines represent negative gravity which push star systems toward the galaxy center, in the same direction that positive gravity, represented by blue lines, pulls. The purple line is the combination of the Newtonian and negative gravity.

One of the reasons MOND has not been widely accepted is because it is a tautology, in other words, it is derived from what it was suppose to explain. However, Curvity, which can encompass MOND, is not a tautology because it is a separate and comprehensive theory.

Link Between Dark Energy and Dark Matter

Curvity suggests a link between Dark Matter and Dark Energy because we can postulate that both result from the same force. Negative gravity from surrounding galaxies pushes other galaxies away, and also pushes the stars within galaxies in the same direction that positive gravity pulls them, toward the center.


  1. Robert P. Kirshner, "The Extravagant Universe: Exploding Stars, Dark Energy and the Accelerating Cosmos", Princeton Science Library, 2002
  2. "They Rode In Space Ships", Gavin Gibbons, 1957, Page 53
  3. "Atoms, Galaxies and Understanding", Daniel W. Fry, Understanding Publishers, Pages 95-97
  4. 2 Ap. J. 1979 vol. 231 p. 659-670 DRESSLER, A. THE DYNAMICS AND STRUCTURE OF THE CD GALAXY IN ABELL 2029
  5. Kirshner, pg 255-256