Normal and dark matter can between them account for some 27% of the total mass/energy of the universe. It appears that the majority, some 73%, must be something else. It is thought to be a form of energy latent within space itself that is totally uniform throughout space. In fact, this could be exactly what was invoked by Einstein to make his ‘static’ universe – the cosmological constant or lambda (Λ) term. A positive Λ term can be interpreted as a fixed positive energy density that pervades all space and is unchanging with time. Its net effect would be repulsive. There are, however, other options and a range of other models are being explored where the energy is time-dependent. These are given names such as ‘quintessence’, meaning 5th force. As the total amount of this energy and its repulsive effects are proportional to the volume of space, the effects of dark energy should become more obvious as the universe ages and its size increases. In all of the Friedmann models of the universe, the initial expansion slows with time as gravity reins back the expansion, and the expansion rate would never increase. However, if there is a component in the universe whose effect is repulsive and increasing with the volume of space, the scale size of the universe will vary in a quite different way with time. Initially, when the volume of the universe is small, gravity will dominate over dark energy and the initial expansion rate of the universe will slow – just as in the Friedmann models – but there will come a point when the repulsive effects of the dark energy will equal and then overcome gravity and the universe will begin to expand at an ever-increasing rate. If this is the case, distant galaxies will be further away from us than would have been the case in the Friedmann models.
Evidence of Dark Energy
The first evidence of dark energy was found in the 1990s. In the 1990s it became possible to measure the distance to very distant galaxies. We can estimate the distance to remote objects if we have what is called a standard candle – an object of known brightness some of which have been observed at known distances nearby. Hubble used such a technique to measure the distances of galaxies using Cepheid variable stars of known peak brightness. These had first been observed in the Small Magellanic Cloud (SMC) at a known distance from us. Suppose one of these stars is observed in a distant galaxy and appears 1/10000th as bright as a similar Cepheid in the SMC. Assuming no extinction by dust it would, from the inverse square law, be at 100 times the distance of the SMC.
However, though Cepheid variable stars are some of the brightest stars known, there is a limit to distances that can be measured by using them. Something brighter is required. For a short time, supernovae are the brightest objects in the universe and there is one variant, called a Type 1a supernova, that is believed to have well-calibrated peak brightness. It might be useful to consider an analogy. Imagine a ball of plutonium of less than critical mass. If one then gradually added additional plutonium uniformly onto its surface it would, at some point in time, exceed the critical mass and explode. The power of this explosion should be the same each time the experiment is carried out as a sphere of plutonium has a well defined critical mass. As you will see, this is rather similar to what occurs when a Type 1a supernova occurs. A Type 1a supernova occurs in a binary system. The more massive star of the pair will evolve to its final state first and its core may become a white dwarf about the size of the Earth. Later its companion will become a red giant and its size will dramatically increase. Its outer layers may then be attracted onto the surface of the white dwarf whose mass will thus increase (Figure 9.13). At some critical point, when its mass nears the Chandrasekhar Limit of roughly 1.44 times the mass of the Sun, the outer layers will ignite and in the resulting thermonuclear explosion, the entire white dwarf star will be consumed. As all such supernovae will explode when they reach the same total mass, it is expected that they will all have similar peak brightness (about 5 billion times brighter than the Sun) and should thus make excellent standard candles. As Type Ia supernovae are so bright, it is possible to see them at very large distances. The brightest Cepheid variable stars can be seen at distances out to about 10–20 Mpc (∼32–64 million light-years).
Detection of Dark Energy
Type Ia supernovae are approximately 14 magnitudes brighter than Cepheid variables and are thus about a quarter of a million times brighter. They can thus be can be seen about 500 times further away corresponding to a distance of around 1000 Mpc – a significant fraction of the radius of the known universe. However, supernovae are rare with perhaps one every 300 years in a typical spiral galaxy. Observations are now being made of thousands of distant galaxies on a regular basis and sophisticated computer programs look for supernovae events. Once initially detected, observations continue to look for the characteristic light curve of a Type 1a supernova which results from the radioactive decay of nickel-56; first to cobalt-56 and then to iron-56. Hubble (and later others) plotted the apparent expansion velocity of galaxies against their distance and produced a linear plot. This plot would not be expected to continue linearly out to very great distances due to changes in the expansion rate of the universe over time. For the critical (or zero curvature) universe which the CMB observations imply, the curve would have been expected to fall below the linear line for great distances. Observations of distant Type Ia supernovae have recently enabled far greater distances to be measured which, together with the corresponding redshifts, have enabled the Hubble plot to be extended to the point where the plot would no longer be linear. As expected, the plot is no longer linear but, to great surprise, the curve falls above the linear extrapolation, not below. This implies that the expansion of the universe is speeding up – not slowing down as expected – and is thus evidence that dark energy exists.
The nature of Dark Energy
Dark energy is known to be very homogeneous, not very dense (about 1029 g cm3) and appears not to interact through any of the fundamental forces other than gravity. This makes it very hard to detect in the laboratory. The simplest explanation for dark energy is that a volume of space has some intrinsic, fundamental energy as hypothesized by Einstein with his cosmological constant. Einstein’s special theory of relativity relates energy and mass by the relation Emc2 and so this energy will have a gravitational effect. It is often called vacuum energy because it is the energy density of the empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum exactly this sort of energy. One can perhaps get some feeling of why a pure vacuum can contain energy by realizing that it is not actually empty! Heisenberg’s Uncertainty Principle allows particles to continuously come into existence and (quickly) go out of existence again. A pure vacuum is seething with these virtual particles!
Connection of Dark Matter & Dark Energy
The equivalence between matter and energy, these small energy fluctuations can produce particles of matter (a particle and its antiparticle must be produced simultaneously) which come into existence for a short time and then disappear. As an example, consider a proton and the antiproton which have masses of 1.7 1024 g. If a virtual pair were to be created, their equivalent energy would be (from Emc2) 3 103 erg and thus they could only exist for a time of order 3 1025 s. A number of experiments have been able to detect this vacuum energy. One of these is the Casimir experiment in which, in principle, two metal plates are placed very close together in a vacuum. In practice, it is easier to use one plate and one plate which is part of a sphere of a very large radius. One way to think of this is that the virtual particles have associated wavelengths – the wave-particle duality. Virtual particles whose wavelengths are longer than the separation of the plates cannot exist between them so there are more virtual particles on their outer sides and this imbalance gives the effect of an attractive force between the plates. An interesting analogy is when two ships sail alongside each other to transfer stores or fuel in the open sea in conditions with little wind but a significant swell. Between them, only waves whose wavelength is smaller than the separation of the hulls can exist but on the outside, all wavelengths can be present. This inequality gives rise to a force that tends to push the two ships apart, thus requiring that the ships actively steer away from each other.
The cosmological constant is the simplest solution to the problem of cosmic acceleration with just one number successfully explaining a variety of observations and has become an essential feature in the current standard model of cosmology. It is called the lambda–cold dark matter model, as it incorporates both cold dark matter and the cosmological constant, and can be used to predict the future of the universe.