PRIMORDIAL ‘RIPPLES’: THE NUMBER Q
The universe was brought into being in a less than fully formed state, but was gifted with the capacity to transform itself from unformed matter into a truly marvellous array of structure and life forms.
St Augustine
GRAVITY AND ENTROPY
In nature, as in music or painting, the most appealing patterns are neither completely regular and repetitive nor completely random and unpredictable, but they combine both these features. The elaborately structured cosmic environment that we see around us is not completely ordered; nor has it run down to an utterly random state. There are ninety-two different kinds of atoms in nature, rather than just the simple hydrogen, deuterium and helium that were forged in the Big Bang. Some of these atoms now find themselves in complex organisms in our Earth’s biosphere; some are in stars; others are dispersed in the voids of intergalactic space. And the temperature contrasts are also immense: the stars have blazing surfaces (and still hotter centres), but the dark sky is close to the ‘absolute zero’ of temperature – warmed to just 2.7 degrees by the microwave afterglow from the Big Bang.
That this intricate complexity all emerged from a boringly amorphous fireball might seem to violate a hallowed physical principle: the Second Law of Thermodynamics. This law describes an inexorable tendency towards uniformity, and away from patterns and structure: things tend to cool if they’re hot, and to warm up if they’re cold. Ink and water can readily mix, whereas the reverse process – stirring a murky liquid until the dye concentrates into a black drop – would astonish us. Ordered states get messed up, but not the reverse. In technical jargon, ‘entropy’ can never decrease. An apparent decrease locally is always outweighed by an entropy increase elsewhere. The classic example of this principle is a steam engine, where the ordered motion of a piston is always accompanied by wasted heat.
We need to rethink our intuitions, however, when gravity comes into play. Stars, for instance, are held together by the inward pull of their own gravity. This is balanced by the pressure of their hot interiors pushing out. Odd though it seems, stars heat up when they lose energy. Suppose that the fuel supply in the Sun’s centre were switched off. Its surface would stay bright because heat diffuses from the even hotter core. If nuclear fusion didn’t regenerate this heat, the Sun would gradually deflate as energy leaked away (within about ten million years, as Lord Kelvin realized in the nineteenth century). But this deflation would actually make the core hotter than before: gravity pulls more strongly at shorter distances, and the central temperature would have to rise in order to provide enough pressure to balance the greater force pressing down on it. Something similar happens when an artificial satellite gradually spirals in to a lower orbit because of atmospheric drag: it heats up, but only half the energy released from gravity goes into heat; the other half goes into speeding up the satellite (because a closer-in orbit is faster).
So it should not surprise us that new stars condense within irregular clouds of cool dusty gas. The densest regions contract because of their own gravity, becoming so compressed that they light up as stars. Exactly how this happens in, for instance, the Orion cloud or the Eagle Nebula, and the proportions of big and small stars that result from this process, are still too hard to calculate even with the biggest computers. (This is why we aren’t sure how many brown dwarf stars there are, which could contribute to the dark matter in our galaxy.) But star formation poses no mystery in principle: once gravity gets a grip on a system, it inexorably contracts.
FROM THE BIG BANG TO GALAXIES
The gas clouds within our galaxy (and within others) have been churned and recycled so much that they retain no ‘memory’ of their origins. Star formation is therefore insensitive to the wider cosmos. But the emergence of the galaxies themselves is less straightforward than the equivalent process for stars. Their origin lies in the early universe; they are shaped by their ‘genetics’ as well as by their environment.
If our universe had started off completely smooth and uniform, it would have remained so throughout its expansion. After ten billion years, it would contain thinly spread dark matter, and hydrogen and helium gas so rarified that there was less than one atom in each cubic metre. It would be cold and dull: no galaxies, therefore no stars, no periodic table, no complexity, certainly no people. But even very slight irregularities in the early phases make a crucial difference, because density contrasts amplify during the expansion. Any patch slightly denser than average decelerates more, because it feels extra gravity; its expansion lags further and further behind that of an average region. (If, by analogy, we throw two balls upwards with slightly different speeds, their trajectories may, to start with, differ only imperceptibly. The slower ball, however, will have completely stopped, and already started to fall, while the faster is still moving upwards.) Gravity amplifies slight ‘ripples’ in an almost featureless fireball, enhancing the density contrasts until the overdense regions stop expanding and condense into structures held together by gravity.
The most conspicuous structures in the cosmos – stars, galaxies, and clusters of galaxies – are all held together by gravity. We can express how tightly they are bound together – or, equivalently, how much energy would be needed to break up and disperse them – as a proportion of their total ‘rest-mass energy’ (mc2). For the biggest structures in our universe – clusters and superclusters – the answer is about one part in a hundred thousand. This is a pure number – a ratio of two energies – and we call it Q.
The fact that Q is so small (of the order of 10−5) means that gravity is actually quite weak in galaxies and clusters. Newton’s theory is therefore good enough for describing how the stars move within a galaxy, and how each galaxy traces out an orbit under the gravitational influence of all the other galaxies and the dark matter within a cluster. The smallness of Q also means that we can validly treat our universe as approximately homogeneous, just as we’d regard a globe as smooth and round if the height of the waves or ripples on its surface were only 1/100,000 of its radius (equivalent to only 60 metres for a globe the size of the Earth).
The ripples would have been imprinted very early on, before the universe ‘knew’ about galaxies and clusters; there would be nothing special about these sizes (or, indeed, about any dimensions that seemed significant in our present universe). The simplest guess would be that nothing in the early universe favours one scale rather than another, so that the ripples are the same on every scale. The degree of initial ‘roughness’ was somehow established when our entire universe was of microscopic size: how this could have happened is conjectured in the next chapter. The number Q is crucial for determining the ‘texture’ of structure in our universe, which would be very different if its value were either much larger or much smaller.
RIPPLES IN THE MICROWAVE AFTERGLOW
Our universe started off dense and opaque, like the glowing gas inside a star. But after half a million years of expansion, the temperature had dropped to around 3000 degrees – slightly cooler than the Sun’s surface. As the universe cooled further, it literally entered a dark age. The darkness persisted until the first protogalaxies formed and lit it up again.
Probing how the dark age ended is a challenge for astronomers in the next decade. Much hope is placed in the proposed ‘Next Generation Space Telescope’. This is planned to have sensitive detectors for red light and infrared radiation, and an eight-metre mirror (compared with only 2.4 metres for the Hubble Space Telescope).
The microwave background radiation, the afterglow from the Big Bang itself, is a direct message from an era when galaxies only existed ‘in embryo’. Slightly overdense regions, expanding slower than average, were destined to become galaxies or clusters; others, slightly underdense, were destined to become voids. And the microwave temperature should bear the imprint of these fluctuations. The expected effect would be about one part in 100,000 – essentially the same number as Q, the fundamental number characterizing the ripple amplitude.
An undoubted cosmological triumph of the 1990s has been the actual mapping of these precursors of cosmic structure. The background microwave radiation is about a hundred times weaker than the emission from the Earth (whose surface temperature is about 300 degrees above absolute zero). The daunting technical challenge is to measure temperature differences a hundred thousand times smaller still. NASA’s COBE satellite, launched in 1990, achieved outstanding accuracy in confirming that the microwaves had a ‘black body’ spectrum (see Chapter 5). It also carried the first instrument sensitive enough to discern that the radiation from some directions was slightly hotter than from others. It scanned the whole sky, measuring the temperature with enough precision to map its non-uniformities.
Measurements of this kind are best made from space because water vapour in the atmosphere absorbs some of the radiation. COBE has been followed up by further measurements, made from mountaintops, from the South Pole (where the water vapour is low) or from equipment flown in balloons. These new experiments can only map a small area – not the entire sky, as a satellite can – but they achieve the same sensitivity at enormously less expense.
The next big advance will, however, come from two spacecraft that will carry more advanced and sensitive sensors than COBE did: NASA’s Microwave Anisotropy Probe (MAP) and the European Space Agency’s Planck/Surveyor. These will, within a few years, yield precise enough data on the ‘roughness’ of the early universe on many different scales, to settle key questions about how galaxies emerged. The microwave background carries a lot of information about the ultra-early universe. It will, for instance, help to pin down Ω and λ, as well as Q.
It was actually a relief rather than a surprise to find non-uniformities in the afterglow temperature at a level of one part in 100,000. If the background microwaves had implied an even smoother early universe, the clusters and superclusters in our present universe would have been a puzzle: there would need to have been some extra force, apart from gravity, that could enhance the density contrasts even faster.
But the fact that Q is only 1/100,000 is really the most remarkable feature of our universe. If you picked up a stone that was spherical to a precision of one part in 100,000, you might wonder what caused the small irregularities but you’d be even more perplexed by the overall smoothness. ‘Inflation’, described in Chapter 9, is the best theory we have of this, and the temperature fluctuations offer important tests of these ideas.
THE EVOLUTION OF ‘VIRTUAL’ UNIVERSES
When the universe was a million years old, everything was still expanding almost uniformly. How did the structures condense out, and develop into the cosmic scene we now observe? Nowadays we can use a computer to study ‘virtual’ universes. At the start of the simulation the material is expanding, but not quite uniformly because irregularities corresponding to the specified value of Q are fed in as part of the initial conditions.
The dominant gravitating stuff is the ‘dark matter’, particles surviving from the early universe that hardly ever collide with each other, but are influenced by gravity. If you averaged over larger and larger volumes, the early universe would have appeared increasingly smooth.1 This means that, were gravity the only relevant force, small scales would condense first. Cosmic structure forms hierarchically, from the bottom up. Swarms of dark matter on subgalactic scales condense out first; these merge into galactic-mass objects, which then form clusters. It takes longer for gravity to reverse the expansion on larger scales.
But this hierarchical clustering in itself leads to a dark and sterile universe. The ‘leaven’ for the universe is the atoms. Their total mass is much less than that of the dark matter: they ride along passively, constituting a dilute gas that ‘feels’ the dark matter’s gravity. But everything we actually see depends on this gas.
The gas behaves in a more complicated way than the dark matter, because gravity isn’t the only force acting on it. Gas ‘feels’ gravity, but it exerts a pressure as well. This pressure prevents the gas from being pulled by gravity into very small ‘clumps’ of dark matter, but gravity wins on scales above a million solar masses. The first gaseous condensations to form – those that would cause the ‘first light’ that ends the cosmic dark age – are consequently a million times heavier than stars. The computer programs used to follow the gas motions resemble those used by aeronautical engineers to study flows around wings and through turbines. Such calculations are deemed reliable enough to be a substitute for wind-tunnel tests; but, even so, computing what happens inside one of these collapsing clouds is much harder, and nobody has yet performed a simulation that starts with a single cloud and ends up with a population of stars. A cloud containing a million solar masses of gas could fragment into a million separate stars like the Sun, or into fewer objects of larger mass. It could even remain in one piece, and contract into a single superstar or quasar.
These first objects would have formed when the universe was only a few hundred million years old – a few per cent of its present age. By the time the universe was a billion years old, galaxy-sized structures would have built up, each an assemblage of stars and held together not only by its own gravity but by the dark matter, which is configured in a ‘swarm’ ten times larger and heavier. Gas continues to fall inwards into these objects and to cool down. If it is spinning, the gas settles into a disc, and condenses into stars, thereby initiating the recycling process that synthesizes and disperses all the elements of the periodic table.
Computer simulations that show at least the broad outline of these processes can be run as movies, depicting the expansion of our universe and the emergence of galaxies about sixteen powers of ten faster than actually happened! Figure 8.1 shows six frames from one such simulation.
Like the individual galaxies, clusters and superclusters are the outcome of gravitational aggregation. The newly formed galaxies would not have been spread completely uniformly – there would be slightly more in some places than in others. As the expansion continued, regions containing excess mass would suffer extra deceleration, so that the galaxies in those regions ended up conspicuously more closely packed than average.2
How can we check whether a virtual universe is indeed an accurate resemblance to our real one? The simulation must mimic the observed properties of galaxies today – their characteristic sizes and shapes, the proportions that are disc-like and the proportions that are elliptical – and the way that they are clustered. But it must do more: it must match the ‘snapshots’ that tell us what galaxies were like, and how they were clustered, at earlier times.
As discussed earlier, the light now reaching us from the remotest galaxies (and which new-generation telescopes can detect and analyse) set out when they were newly formed. And they look different from present-day galaxies. None has yet settled down into steadily spinning discs, and only a small fraction of their constituent gas has yet turned into stars. Most are small: it took successive mergers, and cannibalism by dominant galaxies of their smaller neighbours, to build up the large ones that we see today.
As a by-product of early star formation, something even more interesting happens. Some of the gas settles into the centre of the swarm of dark-matter particles, contracts under its own gravity, and builds up into a ‘superstar’ more than a million times heavier than an ordinary star. Such a big object shines so brightly that its nuclear fuel doesn’t last long; it ends its life not by exploding but by collapsing to form a black hole. Thus, once galaxy formation starts, space gets ‘punctured’ by these holes. Gas continues to fall into them, releasing a power that outshines the rest of the galaxy.
These objects are called ‘quasars’, or ‘active galactic nuclei’, and they are interesting for two reasons. First, they shine more brightly than the galaxies themselves, and therefore serve as probes to illuminate the remote universe. Spectra of quasar light reveal clouds of gas along the line of sight, and yield our best evidence to date for the amount of deuterium – an important check, as we have seen, on the Big Bang theory. Secondly they permit important tests of Einstein’s theory of general relativity. The power they emit comes from material that is swirling very close to a black hole, and perhaps even from the spinning hole itself. There is no real chance of getting an actual image of this flow – it would be even more of a challenge than imaging an Earth-like planet around another star – but the radiation it emits is redshifted by the strong gravity (and this would be additional, of course, to the ordinary cosmological redshift). There would also be large Doppler shifts because of the high speed with which the gas swirls around near the hole (red on the side that is moving away; blue from the approaching gas on the other side). From the inferred motions and gravitational fields, we can test whether black holes have the actual exact properties that Einstein’s theory predicts.
HOW MUCH IS PREDICTABLE?
If one had to summarize, in just one sentence, ‘What’s been happening since the Big Bang?’, the best answer might be to take a deep breath and say: ‘Ever since the beginning, gravity has been moulding cosmic structures and enhancing temperature contrasts, a prerequisite for the emergence of the complexity that lies around us ten billion years later, and of which we are part.’
Once systems form that are heavy enough to be self-gravitating, departures from equilibrium grow. Our universe can thus have evolved from a primordial fireball, uniformly hot, into a structured state containing very hot stars radiating into very cold empty space. This sets the stage for increasingly intricate cosmic evolution, and the emergence of life. Individual stars become denser as they evolve (some ending as neutron stars or black holes), whereas overall the matter gets more thinly spread. These complexities are the outcome of a chain of events that cosmologists can trace back to an ultra-dense primal medium that was almost structureless.
Our view of how cosmic structure emerged is, like the Darwinian view of biological evolution, a compelling general scheme. As with Darwinism, how the whole process got started is still a mystery: the way Q is determined (perhaps as microscopic vibrations in the ultra-early universe) is still perplexing, just as the origin of the first organisms on Earth is. But cosmology is simpler in one important respect: once the starting point is specified, the outcome is in broad terms predictable. All large patches of the universe that start off the same way end up statistically similar. In contrast, the gross course of biological evolution is sensitive to ‘accidents’ – climatic changes, asteroid impacts, epidemics and so forth – so that, if the Earth’s history were rerun, it could end up with a quite different biosphere.
That’s why computer simulations of structure formation are so important. Galaxies and clusters are the outcome of gravity acting on initial irregularities. We don’t try to explain the detailed pattern, only the statistics – just as an oceanographer aims to understand the statistics of waves, not the details of a wave in a single snapshot at a particular place and time.
The starting point is an expanding universe, described by Ω, λ and Q. The outcome depends sensitively on these three key numbers, imprinted (we are not sure how) in the very early universe.
THE TUNING OF Q
The formation of galaxies, clusters and superclusters obviously requires the universe to contain enough dark matter and enough atoms. The value of Ω must not be too low: in a universe that contained radiation and very little else, gravity could never overwhelm pressure. And λ mustn’t be so high that the cosmic repulsion overwhelms gravity before galaxies have formed. There must also be enough ordinary atoms, initially in diffuse gas, to form all of the stars in all of the galaxies. But we’ve seen that something else is needed as well, namely initial irregularities to ‘seed’ the growth of structure. The number Q measures the amplitude of these irregularities or ‘ripples’. Why Q is about 10−5 is still a mystery. But its value is crucial: were it much smaller, or much bigger, the ‘texture’ of the universe would be quite different, and less conducive to the emergence of life forms.
If Q were smaller than 10−5 but the other cosmic numbers were unchanged, aggregations in the dark matter would take longer to develop and would be smaller and looser. The resultant galaxies would be anaemic structures, in which star formation would be slow and inefficient, and ‘processed’ material would be blown out of the galaxy rather than being recycled into new stars that could form planetary systems. If Q were smaller than 10−6, gas would never condense into gravitationally bound structures at all, and such a universe would remain forever dark and featureless, even if its initial ‘mix’ of atoms, dark matter and radiation were the same as in our own.
On the other hand, a universe where Q were substantially larger than 10−5 – where the initial ‘ripples’ were replaced by large-amplitude waves – would be a turbulent and violent place. Regions far bigger than galaxies would condense early in its history. They wouldn’t fragment into stars but would instead collapse into vast black holes, each much heavier than an entire cluster of galaxies in our universe. Any surviving gas would get so hot that it would emit intense X-rays and gamma rays. Galaxies (even if they managed to form) would be much more tightly bound than the actual galaxies in our universe. Stars would be packed too close together and buffeted too frequently to retain stable planetary systems. (For similar reasons, solar systems are not able to exist very close to the centre of our own galaxy, where the stars are in a close-packed swarm compared with our less central locality.)
The fact that Q is 1/100,000 incidentally also makes our universe much easier for cosmologists to understand than would be the case if Q were larger. A small Q guarantees that the structures are all small compared with the horizon, and so our field of view is large enough to encompass many independent patches each big enough to be a fair sample. If Q were much bigger, superclusters would themselves be clustered into structures that stretched up to the scale of the horizon (rather than, as in our universe, being restricted to about one per cent of that scale). It would then make no sense to talk about the average ‘smoothed-out’ properties of our observable universe, and we wouldn’t even be able to define numbers such as Ω.
The smallness of Q, without which cosmologists would have made no progress, seemed until recently a gratifying contingency. Only now are we coming to realize that this isn’t just a convenience for cosmologists, but that life couldn’t have evolved if our universe didn’t have this simplifying feature.