Farewell to Reality

by Jim Baggott

  Dicke presented his arguments in a lecture he delivered at Cornell University in 1978. Sitting in the audience was a young American postdoctoral researcher called Alan Guth, who was struck by the implications:

  The way [Dicke] phrased the problem was that the expansion rate of the universe at one second after the big bang had to be fine-tuned to the accuracy of, I think the number he gave was one part in 1014 [one hundred thousand billion]. And if the rate were one part in 1014 larger than it actually was, the universe would fly apart without galaxies ever forming. And if the universe were expanding at a rate of one part in 1014 slower, the universe would have long ago collapsed.12

  There was another problem. Measurements of the CMB radiation confirmed its astonishing uniformity in temperature across the sky. Now we know that if we place a hot object in contact with a cool object, the temperatures of both objects will equilibrate and become uniform. Such uniformity in temperature implies a dynamic exchange of energy, which can take the form of radiation, between objects that are said to be in ‘causal contact’.

  But the last moment that such an exchange can have taken place was at the moment of recombination, about 380,000 years after the big bang. After that moment, the radiation was freed from matter and would interact with it very rarely. The trouble was, the finite speed of light prevents the entire universe from being causally connected. There would be many regions of the universe more distant than can be reached by radiation travelling at the speed of light, and so these regions could not be in causal contact. There was really no good reason why the temperature of the CMB radiation should be so uniform. This was called the horizon problem.

  The resolution of both the flatness and horizon problems would involve a marvellous fusion of theories of particle physics and cosmology.

  Cosmic inflation

  The discovery of the weak neutral currents at CERN and Fermilab in 1973 lent considerable credibility to the electro-weak theory that Weinberg and Salam had constructed using the Higgs mechanism. At the time, there was no particle accelerator available that could re-create the energies at which the electromagnetic and weak nuclear forces would ‘melt’ back into the single electro-weak force, carried by massless bosons, from which they had originated. But it became entirely reasonable to suppose that such energies would have prevailed in the first moments after the big bang.

  This is now known as the ‘electro-weak epoch’. As the universe cooled, the background Higgs field ‘crystallized’ and the higher symmetry of the electro-weak force was broken (or, more correctly, ‘hidden’). The massless bosons of electromagnetism (photons) continued unimpeded, but the weak force bosons interacted with the Higgs field and gained mass to become the W and Z particles.

  There are close physical analogies between the transitions between these early epochs and the phase transitions of common, everyday substances, such as water. As temperatures fall, steam condenses to liquid water, and the symmetry is reduced as previously free-moving water molecules become connected together in large-scale network structures characteristic of the liquid. As temperatures fall again, water freezes to ice, further reducing the symmetry as the water molecules become locked in a solid crystal structure.

  It required no great leap of logic to suggest that, in an even earlier epoch, the electro-weak and strong nuclear forces would have been similarly joined in a single ‘electro-nuclear’ force.

  In 1974, Weinberg, American theorist Howard Georgi and Australian-born physicist Helen Quinn had shown that the strengths of the interactions of all three particle forces become near equal at energies between a hundred billion and a hundred million billion giga electron-volts (GeV).* These energies, corresponding to temperatures of around ten billion billion billion (1028) degrees, would have been prevalent at about a hundred million billion billion billionth (10-35) of a second after the big bang.

  In this ‘grand unification epoch’, the strong nuclear force and electro-weak force melt into a single electro-nuclear force. All force carriers are identical and there is no mass, no electrical charge, no quark flavour (up, down) or colour (red, green, blue). Breaking this even higher symmetry in theory requires more Higgs fields, crystallizing at higher temperatures and so forcing a divide between quarks, electrons and neutrinos and between the strong and electro-weak forces.

  One of the first examples of such a grand unified theory (GUT) was developed by Glashow and Georgi in 1974.* One consequence of the higher symmetry required by this theory is that all elementary particles simply become facets of one another. Alan Guth confirmed to his own satisfaction that among the new particles predicted by GUTs was the magnetic monopole, a hypothetical single unit of magnetic ‘charge’ equivalent to an isolated north or south pole. In May 1979 he had begun work with a fellow postdoc, Chinese-American Henry Tye, to determine the number of magnetic monopoles likely to have been produced in the big bang. Their mission was to explain why, if magnetic monopoles were indeed formed in the early universe, none are visible today.

  Guth and Tye realized that they could suppress the formation of monopoles by changing the nature of the transition from grand unified to electro-weak epochs. The monopoles largely disappeared if, instead of a smooth phase transition or ‘crystallization’ at the transition temperature, the universe had instead undergone supercooling. In this scenario, the universe persists in its grand unified state well below the transition temperature.**

  When in December 1979 Guth explored the wider effects of the onset of supercooling, he discovered that it predicted a period of extraordinary exponential expansion of spacetime. Initially rather nonplussed by this result, he quickly realized that this explosive expansion could explain important features of the observable universe, in ways that the prevailing big bang cosmology could not.

  When ice melts, the symmetry is increased and the water molecules are freed from their prison in the crystal lattice. A considerable amount of energy in the form of heat is required to complete this phase transition. This heat is used to free the water molecules from their restraints but it does not change the temperature during the transition (which remains fixed at 0°C). The transition is said to be endothermic — it requires the input of thermal energy. Conversely, when water freezes to form ice, this energy or ‘latent heat’ is released and the transition is said to be exothermic — there is an output of thermal energy.

  In supercooled water, the water molecules remain in the liquid state well below the normal freezing point. In this situation the latent heat is not released. It remains latent.

  What Guth found was that if a tiny part of the early post-big-bang universe supercooled at the end of the grand unification epoch, the energy of the Higgs field would remain similarly latent. The energy of the false vacuum so created would instead be pumped into spacetime, acting as a negative pressure and blowing spacetime up exponentially, doubling the size of the universe every ten million billion billion billionth (10-34) of a second. This is Einstein’s cosmological constant on acid.

  ‘I do not remember ever trying to invent a name for this extraordinary phenomenon of exponential expansion,’ Guth later wrote, ‘but my diary shows that by the end of December I had begun to call it inflation.’13

  Eventually, the Higgs field does crystallize and small bubbles of true vacuum start to appear, which cluster together and coalesce. The energy of the Higgs field is released, reheating the now greatly expanded universe, and channelling into the formation of a plasma of quarks, electrons, neutrinos and (mostly) radiation.

  At a stroke, Guth solved two of the most stubborn paradoxes of big bang cosmology. If indeed a tiny part of the universe had supercooled and inflated in this way, then a flat, isotropic, homogeneous visible universe filled with CMB radiation with a uniform temperature was no longer a mystery. It was to be expected.

  Whatever the local curvature of space in that part of the early universe that inflated, inflation would have flattened it. The skin of a deflated balloon may be wrinkled like a prune, curving this way an
d that. Pump it up and the wrinkles are quickly flattened out. The visible universe is isotropic and homogeneous because it comes from a tiny bit of grand-unified universe blown up out of all proportion by inflation. The temperature of the CMB radiation is uniform because, at the onset of inflation, all the contents of the grapefruit-sized universe were in causal contact.

  COBE and WMAP

  Inflationary cosmology underwent some modifications largely as a result of further tinkering with the properties of the Higgs fields used to break the symmetry of the universe at the end of the grand unified epoch. Experimental results gained in the early 1980s provided no support for early GUTs of the Georgi—Glashow type. No longer constrained by theories derived from particle physics, cosmologists were free to fit the observable universe by further tweaking the Higgs fields, which became collectively known as the inflaton field to emphasize its significance.

  Cosmologists began to realize that the seeds of the observable structure of stars, galaxies and clusters of galaxies had to come from quantum fluctuations in the early universe, amplified by inflation.

  Evidence for primeval quantum fluctuations in the inflaton field could be found in the form of tiny variations in the temperature of the CMB radiation. On 18 November 1989, the Cosmic Background Explorer (COBE) satellite was placed into sun-synchronous orbit.*

  The theoretical predictions were borne out in spectacular fashion on 23 April 1992, when a team of American scientists announced that they had found these primeval fluctuations in the data from COBE. The announcement was reported worldwide as a fundamental scientific discovery and ran on the front page of the New York Times.

  These tiny temperature variations have since been measured in even more exquisite detail by the Wilkinson Microwave Anisotropy Probe (WMAP), which was launched on 30 June 2001 and is 45 times more sensitive than COBE. It was originally intended that WMAP would provide observations of the CMB radiation for two years, but mission extensions were subsequently granted in 2002, 2004, 2006 and 2008. WMAP has produced four data releases, in February 2003, March 2006, February 2008 and January 2010.

  Figure 3 shows the map of temperature variations of the CMB radiation across the sky, based on the WMAP seven-year results. In this map, interference from our own Milky Way galaxy has been carefully subtracted out. Different temperatures are shown as different greyscale colours, with white representing a higher temperature and black representing a lower temperature. The total temperature variation from white to black is just 200 millionths of a degree.

  Figure 3 A detailed, all-sky image of temperature variations in the cosmic microwave background radiation based on 7-year WMAP data. The temperature variations are of the order of ± 200 millionths of a degree and are shown as greyscale colour differences. They represent quantum fluctuations that became ‘frozen’ in the background radiation when this disengaged from matter about 380,000 years after the big bang and acted as seeds for subsequent galaxy formation. NASA/WMAP Science Team.

  If the temperature variations from point to point appear random in this picture, it is because this is precisely what they are. The variations are due to quantum fluctuations in the inflaton field predicted, to an accuracy of one part in 10,000, by the theory of inflation.

  From their vantage points in earth orbit, COBE and WMAP have detected the signature of quantum uncertainty in the birth of our universe, a signature written 13.7 billion years ago.

  Dark matter

  Inflation resolved some of the paradoxes of big bang cosmology, but it came with a significant trade-off. It seems that only a tiny part of the universe inflated at the end of the grand unified epoch to form the flat universe we now inhabit. We therefore have to reconcile ourselves to the fact that our observations are limited to this visible universe, our own local bubble of inflated spacetime. There may be much, much more to the larger universe, perhaps consisting of many other bubbles. We will likely never know.

  This is a sobering thought, but we shouldn’t dwell on it too long. We may be limited in terms of the scope of our vision, but there’s still much to do.

  The Coma cluster is a large galactic cluster located in the constellation Coma Berenices. It contains over a thousand identified galaxies. In 1934, the Swiss astronomer Fritz Zwicky estimated the cluster’s total mass from observations of the motions of galaxies near its edge. He then compared this to another estimate based on the number of observable galaxies and the total brightness of the cluster. He was shocked to find that these estimates differed by a factor of 400.* The mass, and hence the gravity, of the visible galaxies in the cluster is far too small to explain the speed of the orbits of galaxies at the edge.

  As much as 90 per cent of the mass required to explain the size of the gravitational effects appeared to be ‘missing’, or invisible. Zwicky inferred that there must be some invisible form of matter which makes up the difference. He called it ‘missing mass’.

  Missing mass was acknowledged as a problem but lay relatively dormant for another forty years. In 1975, the same problem was identified in the context of the motions of individual galaxies by young American astronomer Vera Rubin and her colleague Kent Ford. They reported the results of meticulous measurements of the speeds of stars at the edges of spiral galaxies. What they discovered was that stars at the edge of a galaxy move much faster than predicted based on estimates of the mass of the galaxy derived from its visible stars.

  Simple Newtonian gravity predicts that the further the star is from the centre of the galaxy where most of the stellar mass is concentrated, the weaker the force of gravity that drags it around. Consequently, the speeds of stars being dragged around the centre would be expected to fall the further they are from the centre. Rubin and Ford found that the speeds of the stars actually level off the further they are from the centre.

  Although Rubin’s results were initially greeted with scepticism, they were eventually accepted as correct. In fact, Peebles and his Princeton colleague Jeremiah Ostriker had earlier concluded that the observed motions of galaxies (including our own Milky Way) could not be modelled theoretically unless it was assumed that each galaxy possesses a large halo of invisible matter, effectively doubling the mass. In 1973 they had written: ‘… the halo masses of our Galaxy and of other spiral galaxies exterior to the observed disks may be extremely large’.14 The following year they suggested that the masses of galaxies might have been underestimated by a factor often or more.

  The missing matter was now ‘dark matter’.

  It is now thought possible to account for a small proportion of dark matter using exotic astronomical objects composed of ordinary matter which emit little or no radiation (and are therefore ‘dark’). These are called Massive Astrophysical Compact Halo Objects, or MACHOs. Candidates include black holes or neutron stars as well as brown dwarf stars or unassociated planets.

  However, the vast majority of the dark matter is thought to be so-called ‘non—baryonic’ matter, i.e. matter that involves not protons or neutrons, but most likely particles not currently known to the standard model of particle physics. Such particles are called Weakly Interacting Massive Particles, or WIMPs.* They have many of the properties of neutrinos, but are required to be far more massive and therefore move much more slowly.

  Dark energy and the return of the cosmological constant

  In 1992, the COBE satellite revealed the imprint of quantum fluctuations on the early universe and confirmed, with some confidence, that the universe is flat. Cosmic inflation could explain why this must be so.

  But a density parameter Ω equal to 1 demands that the universe should contain the critical density of mass-energy. The problem was that, no matter how hard they looked, astronomers couldn’t find it. Even dark matter didn’t help. In the 1990s, the best estimate for Ω based on the observed (and implied) mass-energy of the universe was of the order of 0.2. If this were really the case, the universe should be ‘open’. With insufficient mass-energy to halt expansion, it would be destined to expand for ever.

/>   Some astrophysicists began to mutter darkly that Einstein’s infamous fudge factor — the cosmological constant — might after all have a place in the equations of the universe. Several earlier attempts had been made to resurrect it, but it had stayed dead. Now some were beginning to appreciate that a mass-energy density of 0.2 and a cosmological constant contributing another 0.8 might be the only way to explain how Ω can be equal to 1 and why the universe is flat.

  To predict the ultimate fate of the universe, astronomers first have to learn as much as possible about its past. To learn about the past, it is necessary to study the most distant objects visible. Light from distant objects shows us how these objects were behaving at the time the light was emitted (for example, light from the sun shows us how the sun looked about eight minutes ago; light from the Andromeda galaxy shows us how it was 2.5 million years ago).

  Because the speed of light is finite, it takes some time for this light to reach us here on earth. So when we study the light from objects at the edges of the universe, we take a journey into the distant past.

  The attentions of astronomers turned to supernovae, first discovered by Zwicky in the 1920s. These occur when a star exhausts its nuclear fuel and can no longer support itself against the force of gravity. The star collapses. This collapse may trigger a sudden release of gravitational energy, blowing the star’s outer layers away in a massive stellar explosion. Or, under the right conditions, a so-called white dwarf star consisting mostly of carbon and oxygen may gain sufficient mass to trigger runaway carbon fusion reactions, resulting in a similar cataclysmic explosion.

  For a brief time, a supernova may outshine an entire galaxy, before fading away over several weeks or months.

  Astronomers classify supernovae based on the different chemical elements they are observed to contain from their absorption spectra. Supernovae involving stars that have exhausted their hydrogen are called Type I. These are further subcategorized according to the presence of spectral lines from other atoms or ions. Type Ia supernovae produce no hydrogen absorption lines but exhibit a strong line due to ionized silicon. They are produced when a white dwarf star accretes mass (perhaps from a neighbouring star) sufficient to trigger carbon fusion reactions.