The Dark Universe

by Dr. Geoffrey Dobson

Introduction

At the end of the twentieth century astrophysicists proposed that 96 percent of the matter in our universe is unknown and so far undetectable by us. The search is on to find “dark matter” and “dark energy”. Whoever finds them will be hailed as the saviours of modern astrophysics. We got into this ghastly position because modern instrumentation lets us make much more accurate measurements of the movement of distant galaxies and the stars within them. It seems that their behaviour does not conform to the predictions of either Newton’s law of gravity or Einstein’s theory of General Relativity. Such a prospect is so unthinkable that the physicists have invented the new types of matter to make the theories work. This is not unheard of in particle physics and has been done many times before. Usually the proposed particles like the Higgs Boson have been subsequently found in particle accelerators and everyone has breathed a huge sigh of relief.

Accepted theories of Gravity

Newton’s theory of gravity states that the attractive gravitational force between two bodies is proportional to the product of their two masses and inversely proportional to the distance between them. The theory was extraordinarily successful in predicting the elliptical orbits of planets around the sun that had been observed by Kepler, with one minor exception in that there were small discrepancies between the calculated and observed orbits of Mercury. The theory survived unchallenged until Einstein introduced the General Theory of Relativity in 1917. Even today Newton’s theory is still used by NASA to compute the trajectories of their spacecraft.

General Relativity describes gravitational force in terms of the warping of space-time around massive bodies like the sun. Gravity and acceleration are assumed to be equivalent to each other in producing the experience of a force. It contains Newton’s law as an approximation but also predicted many new phenomena caused by strong gravitational fields. These include the bending of light beams, clocks running slow, the spectrum of light being red shifted, the collapse of giant stars under their own gravity to make black holes, and gravitational forces transmitted through space as waves moving at the speed of light . All these effects were subsequently confirmed. Today physicists are seeking to develop a new theory because General Relativity does not incorporate Quantum Mechanics and so it is not possible to unite gravity with the other known forces in nature. General Relativity is regarded as one of the greatest intellectual achievements of the twentieth century, so that any idea that it might be wrong is far too scary to consider.

Dark Matter

The modern controversy about gravity started in 1933, when astronomers first noticed that stars in the outer rings of galaxies were moving faster than expected for the size of the galaxies. You can estimate how much mass there is in a galaxy from how much light it emits, so you can calculate the gravitational forces within it, and thus how fast stars should be moving in their orbits. If the stars are going too fast it means that there should be far more mass in the galaxy than you calculate, but we can’t see it. The amount of visible mass present in observed galaxies is nowhere near enough to prevent them flying apart. By 1970 most astronomers were convinced that we have not detected 96 percent of the matter holding the galaxies together. The Dark Matter is thought to be in a halo around each galaxy because only the outer stars of the galaxy are anomalous. The inner stars seem to follow orbits corresponding to Newtonian calculations
The particles that make up dark matter must be stable heavy particles that have no charge or strong interactions with other particles, but only gravitational effects. They are called WIMPs short for “weakly interacting massive particles”. Symmetry broken versions of the standard model of quantum field theory do in fact include such a particle called an “axion”. By definition there is no way to directly observe the WIMPs. Particle physicists are looking for dark matter as asymmetries in the way that particles move in the Large Hadron Collider. . Astronomers are searching for dark matter in the universe by observing the way that galaxies cluster into clumps.

Dark Energy

The plot thickened in 1998 when astrophysicists started measuring the speed at which distant galaxies are moving away from us. If we add all the necessary dark matter for stabilising galaxies to the known total mass of the visible universe and put the result into the Einstein gravitational field equations, we conclude that the rate of expansion of the universe should be decelerating. In fact the most recent measurements show that the rate of expansion is accelerating. Astronomers have therefore been forced to revive Einstein’s cosmological constant to account for this. They speculate that the origin of the cosmological constant is “dark energy” providing an anti-gravitational force. The force is negligible at short distances like within our solar system but becomes stronger at intergalactic distances. The cosmological constant has the perfect characteristics to describe dark energy, but what is it?

The gravitational field equations in General Relativity essentially express a balance between expansionary forces due to the energy and entropy of the cooling universe and gravitational forces in a curved space-time. At the time that Einstein first developed the gravitational field equations for General Relativity the universe outside our own milky way was unknown and the universe was thought to be unchanging and eternal. It was very difficult to achieve a constant “closed” universe in the equations. Einstein thought that as the universe cooled down, gravity would eventually overwhelm the energy forces and cause the universe to contract. He therefore introduced an extra term in the equations known as the “cosmological constant”. This was really a sort of fudge factor that could be adjusted to keep the universe unchanging and closed. If the constant was positive the new term corresponded to a sort of anti gravitational energy that would keep the universe expanding. If the constant is negative there is an extra gravitational force causing contraction. By adjusting the constant we can have an expanding, constant or contracting universe. The term in the gravitational field equations was formulated so that any force due to the cosmological constant would be very weak at short distances such as between the planets in our solar system, but would become progressively stronger at intergalactic distances.

Theorists at the time criticised the cosmological term as an ugly addition that did not fit into a beautiful equation. They also had no idea what would be the origin of the new force. When in 1929 Hubble discovered that the universe was indeed expanding at an apparently uniform rate, they concluded that there was no need for the cosmological term. Einstein was horrified and recanted. He described the introduction of the cosmological constant as “the biggest mistake of my life” and deleted the additional term in the gravitational field equations. However when Friedman developed several working models for the universe from Einstein’s gravitational field equations, he showed that in every case that, without the cosmological term, the rate of expansion of the universe would slow down and finally turn into a contraction. The cosmological term was revived and astrophysicists began searching for more accurate and detailed measurements of the rate of expansion of the universe. Today the cosmological constant describes perfectly the dark energy so has finally achieved full respectability.

Quantum field theory predicts that the vacuum of space is filled with a uniform field of “zero point energy” corresponding to the remaining energy when all the particles in the vacuum are in their lowest possible energy state. This vacuum energy has no effect in normal quantum mechanical interactions, so is removed from the calculations by the process of “renormalisation”. However it does have exactly the right properties to be dark energy. There is a problem however in calculating how much vacuum energy there is in the vacuum of space. Quantum mechanical calculations of the zero point energy result in a vacuum energy that is too large by a factor of 10120. Recent textbooks have described this as “the worst calculation in the history of physics”. Theorists are seeking some rule of renormalisation to apply to calculating dark energy from vacuum energy but so far without success. (In practical situations only differences in energy can be detected. Since the zero point field is constant everywhere it can be subtracted from the calculations. This is renormalisation.)

Alternative Theories (MOND)

In 1981 Mordehai Milgrom threw a cat among the pigeons by reviving an old idea that maybe Newton’s universal inverse square law of gravity does not hold for inter galactic distances. Instead they proposed that at very long distances, forces start to decay in a linear way with distance so that gravity is stronger at long distances than you would expect. The idea was enthusiastically adopted by astronomers Stacy McGaugh and Vera Rubin. This theory is called Modified Newtonian Dynamics or MOND. If this is true there is no need to invoke any existence of Dark Matter. For a long time hardly anyone took this idea seriously because it violated the theory of Special Relativity, so it not only insulted Newton but also Einstein. Then in 2004 a brilliant young physicist Jacob Berkstein developed a relatavistic version of MOND, and suddenly it became respectable.

The position today is that the mainstream of astronomers believe in Dark Matter, but a small but significant minority do not like the idea of introducing exotic particles that we have no means of detecting just to make the equations work. Maybe one day it will all be resolved by the LHC but do not hold your breath!!

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