Big Crunch Universe

DARK ENERGY AND THE RED SHIFT IN A CONTRACTING UNIVERSE

Stephen A. McSween, November 2015

In 1929 Edwin Hubble discovered that the light from most galaxies visible from Earth was Doppler shifted to the red and that the intensity of the red shift was directly proportional to distance. This meant that the distance between the Earth and most galaxies was increasing and that the greater the distance between them, the faster they were moving apart. Based upon this finding, cosmologists concluded that the universe was expanding. Overlooked was the fact that from the perspective of one inside the universe such as an astronomer on Earth, the light from most galaxies in a “Big Crunch” contracting universe would also be shifted to the red exactly as Hubble observed. Moreover, the exaggerated red shifts currently attributed to Dark Energy are easily explained by the Big Crunch model. Therefore, the conclusion that the universe is expanding rather than contracting should be reconsidered.

The “Big Crunch” Model of a Contracting Universe

In a letter to Cambridge philosopher Eric Bentley in the 1600’s, Sir Isaac Newton noted that the combined gravitational attraction of all of the stars should cause them to fall together towards a single point. This came to be known as Bentley’s Paradox. Though he favored the static model, Einstein realized that this would require “a sort of antigravity that pushed outward just hard enough to balance the gravity that was trying to pull it inward.” Therefore, he added an expansionary cosmological constant to his general theory of relativity published in 1917. With Hubble’s discovery of the red shift in 1929, Newton and Einstein’s concerns about a contracting universe were dismissed in favor of the expanding model.

In Stephen Hawking’s magnificent 1988 book A Brief History of Time, he points out that a “Big Crunch” contracting universe is one of only three models that obey Alexander Friedman’s two fundamental assumptions about the universe and is the only model discovered by Friedman himself. Hawking describes the Big Crunch model as follows:

“In the first kind (which Friedman found) the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop. The galaxies then start to move toward each other and the universe contracts. Figure 3.2 shows how the distance between two neighboring galaxies changes as time increases. It starts at zero, increases to a maximum, and then decreases to zero again.”

With the acceptance of the expanding model, the mechanics of how the distance between the galaxies in Friedman’s Big Crunch model would return to zero were never explored. The “how” is important because if the universe is contracting around a singularity like a large black hole, then gravity alone will account not only for Hubble’s redshift but also for the exaggerated red shifts currently attributed to Dark Energy and other unexplained phenomena.

I. The Red Shift in a Contracting Universe

In the early 1900’s, the consensus favored a static model of the universe over an expanding or contracting one. The consensus shifted to the expanding model upon Hubble’s discovery of a red shift directly proportional to distance in the light from most galaxies observable from Earth. A necessary but unstated corollary to that conclusion was that the light from most galaxies observable from Earth in a contracting universe would be blue-shifted. This corollary is false. Instead, in a universe contracting around a Cosmic Singularity, the light from most galaxies visible from Earth (within the Earth’s light cone) would also be shifted to the red just as Hubble observed. Here’s why:

1. The gravitational pull of the Singularity would be stronger on those galaxies closer to the Singularity than on those galaxies farther away.
2. This difference in gravitational pulls would cause the closer galaxies to be moving faster towards the Singularity than the farther galaxies causing the distance between the closer and farther galaxies to be increasing.
3. The increasing distance between the closer and farther galaxies would cause a Doppler shift to the red in any light passing between them.
4. Since, as between the Earth and most any galaxy within the Earth’s light cone, one would be closer to the Singularity than the other and, therefore, moving faster towards the Singularity than the other, the distance between the Earth and most any galaxy visible from Earth would be increasing causing a Doppler shift to the red in any light passing between them.
5. Moreover, the greater the distance between the Earth and the galaxy, the greater the difference in the gravitational pull of the Singularity on each resulting in an increase in direct proportion to distance in the speed at which they are moving apart and in the corresponding intensity of the redshift in any light passing between them.
6. There is nothing unique about Earth’s perspective. The light from most galaxies visible from any other point within a contracting universe (other than the Cosmic Singularity itself) would also be shifted to the red in direct proportion to distance.

Consider the common raisin bread analogy for an expanding universe. If one were to film the rising loaf, one would record an excellent example of a red-shifted expanding universe because, as the dough rises, the distance between all of the raisins would be increasing in direct proportion to the distance between them. If one were to then view the film in reverse, one would see an excellent example of a blue-shifted contracting universe because the film would show the exterior raisins moving faster towards the center of the loaf than the interior raisins as they race to reach the center at the same time causing the distance between most all the raisins to be decreasing. However, the reversed film would bear no resemblance to a Big Crunch universe contracting around a Singularity. To mirror a Big Crunch universe, the raisins closer to the center of the raisin bread would have to be moving faster towards the center than the exterior raisins to model the stronger gravitational pull of the Cosmic Singularity on the interior raisins. This difference in speeds would cause the distance between the exterior and interior raisins to be increasing – resulting in a red shift proportional to distance in any light passing between them – even though they will all end up in the center.

In this way, a Big Crunch universe in which the galaxies are all contracting under the gravitational pull of a Cosmic Singularity would behave very much like a large black hole. Kip S. Thorne illustrates and describes the action around a typical black hole as follows:

The atoms of gas that sparsely populate interstellar space, approximately one in each cubic centimeter, are being pulled by the hole’s gravity. They stream toward the hole from all directions, slowly at great distances where gravity pulls them weakly, faster nearer the hole where gravity is stronger, and extremely fast – almost as fast as light – close to the hole where gravity is strongest. Kip S. Thorne, black holes & Time Warps: Einstein’s Outrageous Legacy (Norton, 1994) p.24.

By substituting “galaxies” for “atoms of gas” in Thorne’s description, one can see that the closer galaxies would be travelling faster towards the Singularity than the farther galaxies causing the distance between them to be increasing and a red shift in the light passing between. Pick an arrow in Thorne’s illustration to represent our galaxy and draw a circle around it to represent the Earth’s light cone. You can see that the distance between our galaxy and most any galaxy visible from Earth would be increasing even as they are both being pulled by gravity towards the Singularity. Only relatively close galaxies equidistant from the Cosmic Singularity with our galaxy would be moving closer to our galaxy causing the light between them to be blueshifted. This predominant red shift is exactly what researchers have found when modeling the motion of objects below the event horizon of a black hole. “According to Hamilton and Polhemus, inside a black hole the view in the horizontal plane is highly blueshifted, but all directions other than horizontal appear highly redshifted.” MIT Technology Review

Though counter-intuitive, the gravitational pull of the Cosmic Singularity would cause the distance between most galaxies within one another’s light cone to be increasing – causing a red shift in any light passing between them directly proportional to distance – even as they are all being pulled towards the Singularity.

II. Dark Energy in a Contracting Universe

In 1998, with the help of more accurate measurements of distance, astronomers found that the red shift in the light from distant galaxies was greater than a linear increase over distance would predict. From this they concluded that the rate of expansion of the universe was accelerating. There being no known force which could cause the acceleration, cosmologists posited an unexplained force called “Dark Energy” as the cause. In a Big Crunch contracting universe, these exaggerated red shifts attributed to Dark Energy would simply be the predictable result of the difference in the intensity of the gravitational pull of the Singularity over distance:

1. Per Newton’s Universal Law of Gravitation, the gravitational force between any two objects is directly proportional to the product of their masses but inversely proportional to the square of the distance between them.
2. This means that in a Big Crunch universe, a galaxy twice as far from the singularity as a galaxy of similar mass will experience only 1/4 of the singularity’s gravitational pull, a galaxy 4 times as far from the Singularity as a similar galaxy will experience only 1/16th of the gravitational pull, and so on.
3. As a result, a galaxy 1/2 as far from the Singularity as a similar galaxy would be travelling 4 times faster towards the Singularity while a galaxy 1/4 as far from the Singularity as a similar galaxy would be traveling 16 times faster towards the Singularity.
4. These exaggerated (greater than linear) differences in the speed at which the galaxies are being pulled towards the Singularity over distance would, in turn, cause not only a red shift in the light passing between them but the exaggerated red shifts currently attributed to Dark Energy.
5. To illustrate, assume two galaxies of similar mass visible from Earth in the general direction of the Singularity with Galaxy B being twice as far from Earth as Galaxy A. The gravitational pull of the Singularity would be greater on Galaxy B than on Galaxy A causing Galaxy B to be moving faster towards the Singularity than Galaxy A. Therefore, an astronomer on Earth would observe a redshift in the light from Galaxy A and a greater redshift in the light from Galaxy B, but the redshift in the light from Galaxy B would be greater than twice the redshift in the light from Galaxy A. This is because, per Newton’s Law, the difference between the gravitational pull of the Singularity on the Earth vs. Galaxy B would be greater than twice the difference in the gravitational pull of the Singularity on the Earth vs. Galaxy A.

Therefore, in the contracting phase of a Big Crunch universe, the exaggerated red shifts currently attributed to Dark Energy would be caused by simple gravity.

III. Dark Matter in a Contracting Universe

Astronomers have long observed certain gravitational effects in the rotation of galaxies for which the visible matter in the universe cannot account. These effects are so pervasive that to account for them it is estimated that four-fifths of all matter in the universe is made up of an invisible substance called “Dark Matter.” Efforts to detect theoretical Dark Matter particles known as WIMPS – including the LUX Dark Matter Experiment and the Large Hadron Collider – have to date been wholly unsuccessful. In a Big Crunch contracting universe, the massive gravitational pull of the Cosmic Singularity on all matter in the universe could account for the unexplained gravitational effects currently attributed to Dark Matter.

IV. Coalescence of Matter into Stars and Planets

In the midst of an accelerating expansion of the universe, there is no ready explanation for a gravitational force strong enough to cause matter to coalesce into stars and planets. In the contracting phase of a Big Crunch universe, there is no accelerating expansion for gravity to overcome. Even the formation of the recently discovered massive black hole the size of 12 billion suns only 875 million years after the Big Bang could be more easily explained in the context of a Big Crunch contracting universe.

V. The Slowdown and Speed Up of the Expansion of the Universe

The expansion of the universe appears to have gradually slowed for the first several billion years after the Big Bang, but then to have sped up. Having no other explanation, cosmologists have credited the “repulsive effects” of Dark Energy for this phenomenon. In a Big Crunch model, the expansion of the universe following the Big Bang is slowed by gravity causing the universe to transition from expansion to contraction. This could account for the apparent slowdown. The redshifts evidencing the Speed Up could simply be the exaggerated redshifts caused by the gravitational pull of the Cosmic Singularity as previously explained.

VI. Reasons of Symmetry and Consistency

There are other less scientific reasons for favoring the Big Crunch model. First, per general relativity, the universe began as a singularity at the start of the Big Bang. For it to end as a singularity as the distance between the galaxies once again returns to zero exhibits a certain symmetry which is appealing. Second, the consistent pattern of the universe is that of objects arrayed around a central gravitational source. Moons revolve around planets, planets around stars, and stars around super massive black holes in the center of galaxies. In the expanding model, the galaxies alone are untethered to any central gravitational source. But in a Big Crunch universe, the galaxies, too, are arrayed around a central gravitational source – the Cosmic Singularity.

Conclusion

Of course, the galaxies in a contracting universe would not be traveling towards the Cosmic Singularity on straight paths like spokes on a bicycle wheel any more than the galaxies in an expanding universe would be traveling on straight paths away from the Big Bang. Instead the galaxies would be following disparate paths towards the Singularity resulting in some variation in the red shift of the light passing between them and even some blue shifts as the paths of two galaxies are temporarily bringing them closer together. However, so long as the gravitational pull of the Cosmic Singularity is the dominant organizing force on all matter in a contracting universe – just as the Big Bang is the dominant organizing force on all matter in an expanding universe – the distance between most galaxies visible to one another will be increasing causing a Doppler shift to the red in any light passing between them directly proportional to distance. Only from the vantage point of the Cosmic Singularity itself would the light from most galaxies in a contracting universe be blue-shifted – because there the universe really would be falling in on you.