In this section we look at the deep origins of structure — how did the Universe ever become lumpy? Remarkably, the answer lies in the quantum world.
At this point, our story takes a new turn – one which brings us into an almost surreal world of magic and miracles. If you felt lost in the remoteness of the microwave background and those early years of expanding glowing pulsing fog, brace yourself for an unimaginably more alien world, one so far back in Nature's youth that even the language of physics was unrecognizable. But like the old-English of Beowulf, what seems at first unintelligible, ultimately yields a new and breathtaking story.
The reason we need to visit this utterly remote and magical time is simple enough. In tales of origins, one must retrace the causal path back to ever earlier times: what caused the cause which caused the world to be the way it is. In our case, we want to know what caused the seeds of sound. What struck the cosmic bell to set it ringing. Back in Topic 5 we talked about "the origin of sound" – how gravity pulled gas into "valleys" away from "hills", and how pressure led to acoustic oscillations which became the first sound waves. But this is only one step in a deeper story – it does not describe the ultimate origin of sound. We want to know why there were hills and valleys; why was the gravitational landscape uneven? Our focus shifts from the origin of sound to the origin of roughness.
The search for the origin of roughness has been a long and difficult one, and ends almost at the beginning of time. Let's follow some of that story now....
The origin of roughness has proved a hard nut to crack. It is also a tricky subject to follow because it can seem confusingly paradoxical. First one learns that the laws of physics demand that the Universe should be staggeringly smooth; then one learns that the laws of physics demand that the Universe should be staggeringly lumpy. Since the real Universe is neither of these – it's just modestly lumpy – something is clearly missing. The missing ingredients, which provide a solution to the paradox, are found in the seemingly magical worlds of quantum mechanics and cosmic inflation. Before jumping into those worlds, let's first absorb the nature of the paradox.
With all our talk of CMB patchiness, you may have forgotten that the CMB's most basic property is uniformity — the early Universe was extremely smooth. Could it be, perhaps, that the Universe simply started out life exactly smooth, and then gradually grew lumpy with time? Is this possible? Do processes exist which can generate lumpiness out of smoothness, perhaps aided by expansion?
After much hard work, cosmologists concluded the answer is no, at least not with "normal" expansion, the kind occurring today. Here are two possible processes, both of which fail miserably. First, since matter is ultimately made of particles, then randomness alone will ensure at least some granularity – a small volume over here may contain 1000 protons while the same volume over there may contain 1025. Could this statistical randomness grow to significance? Alas no. Even though larger volumes have larger differences in their particle populations, the percentage difference is less, and such differences are way too small to grow, either by expansion or gravity. A similar result is found if the seed variations are not just statistical, but quantum mechanical instead – an inherent granularity in all processes.
As far as we know, if the Universe began smooth and expanded normally, then it would still be smooth, and there would be no stars, galaxies, or people. Since all these exist, then either the Universe began lumpy or its expansion history was radically different. Or both.
Having raised the possibility of a smooth initial Universe, there are in fact powerful reasons to expect the infant Universe to be exceedingly lumpy. Why? Because an instant after the beginning of time, different parts of the Big Bang were profoundly independent, having never been in contact. Recall Topic 13: no signal or force can travel faster than light, so 10 minutes after the Big Bang two regions separated by more than 10 light minutes are oblivious of each other – they are causally unconnected. They could only be similar if different parts of the Big Bang happened to burst forth with similar properties. While it's true that we have no idea "why" there was a Big Bang, almost any notion of causality sees such synchrony at the moment of creation as deeply "spooky." Instead, it seems much more likely that radically independent regions should emerge with radically independent properties.
What do observations reveal – is the Universe lumpy on super-horizon scales? One way to check is to look back to a time when the horizon size was much smaller than it is today. The CMB, for example. At that time, the horizon size was only 400,000 light years – about 2° on the sky. Following our discussion, the CMB should be very blotchy across most of the sky. The fact that it is highly uniform constitutes a classic problem – called "the horizon problem" – and was one of the primary reasons to push for a radically new description of the very early Universe....
In the early 1980s a bold new idea was introduced – cosmic inflation – that at one stroke solved several serious problems, including both the horizon and structure problems. What is inflation, and why is it such a panacea? This is where we enter the bizarre – and poorly understood – realm of the exceedingly young Universe.
An unimaginably short time after creation, the freshly minted space of the newborn Universe was still "live" – it contained a latent energy, waiting to be released. And released it was – in a breathtaking instant the vacuum relaxed, liberating an energy which drove an astonishingly fast expansion. This expansion was unlike our current coasting expansion – it was exponentially accelerating, and inflated the Universe by an enormous factor, possibly as much as 1050. For our purposes, this type of expansion has two wonderful properties.
Those last two brief statements hide some extraordinary truths, which it would be criminal not to develop. Fully grasping these should leave you a little stunned.
First, all structures in the Universe, from stars to galaxies to the cosmic web, arise from sub-sub-microscopic quantum fluctuations. Colossally amplified by inflation, this imperceptibly fine froth of Nature yielded the very seeds which ultimately grew into galaxies. What poetic notions – the largest objects in the Universe come from the smallest; and all structure has roots in the quantum world, without which the Universe would be forever smooth and silent, dark and lifeless.
Second, this explanation for the origin of all structure also answers the philosophical riddle of infinite causal regression. Quantum fluctuations are a-causal, since they are deeply random. In a sense, they are a true first cause – the start of a chain of cause and effect which ultimately ends with the Sun and stars, me and you.
Third, inflation makes the Universe vastly bigger than previously imagined. If our entire visible Universe was once a sub-horizon patch in the otherwise chaotically lumpy Big Bang, then "out there" beyond our current 14 billion light year horizon lie countless regions of space, each as large or larger than everything we now see.
Imagine the scene an instant after inflation: a brilliant incandescent sea of thick fluid, flying away into an infinite invisible distance – smooth and quiet, powerful and live. Turn up your senses to feel all around the subtlest of variations — a little brighter here, a little dimmer there. These freshly minted variations come in all shapes and sizes, a relic from before inflation, an unnatural trespass of the quantum world into the cosmic. It's almost as if you've shrunk to sub-proton size to witness quantum chaos first hand; though in reality the reverse has happened – the invisibly minute quantum froth has rushed up and out in scale, dwarfing us en route, to land with cosmic proportions – huge yet barely perceptible, quietly latent, waiting for the metamorphosis that is to come – to sound, to stars, to galaxies, to everything. The stage is set, the players are in place, and the script written – time alone will now carry the play to its conclusion.
Although this world is still quiet, it is itching to break the silence. The clumps were created on the brink of making sound – poised, frozen, ready to fall into themselves. So what holds them back, what are they waiting for? Strangely, they must first become "aware" of their own existence. Like a dawn bugle whose sound spreads across a sleeping camp, a gravitational wake-up call spreads out at light-speed, rousing all in its path. Once awake and aware, motion starts, and sound begins.
The sound which grows as the Universe awakens is the sound which this project has focused on, and tried to render audible to human ears. But what about that initial scene, when all the amplified quantum variations were in place, frozen, waiting to move. Although all is deathly quiet, there is present throughout the entire Universe an exceedingly rich latent sound ready to burst forth, simply waiting for gravity's order to arrive. In a sense, space was filled with a silent sound, a silence so rich that within it all future sounds were already present. If we could somehow cheat time, and unlock all this sound at once, what would it sound like? What a bold aim – to render audible this opening silence, pristine and raw, unaltered by gravity or time – the ultimate source of all that is to come. Surely, it will be an enthralling sound?
Before we attempt this, let's recall the heritage of the opening sound – it comes from the quantum world. In a sense, we are listening to quantum noise, rendered audible by Nature's stupendously powerful hi-fidelity amplifier – inflation. This is a staggering concept – Big Bang acoustics provides an opportunity not only to listen to the largest vibrations in the Universe, but also to the smallest. We'll return to this theme somewhat differently in Topic 15.
So, let's begin. To unlock that opening sound, all we need is its "sound spectrum"...
As you might imagine, one of the holy grails of modern cosmology is to find the sound spectrum of that first post-inflation moment, before gravity had time to change anything. Cosmologists call this "The Initial Power Spectrum", and its form determines, in large part, how the Universe will ultimately evolve. In a sense, it is a major ingredient of the cosmic DNA.
At the present time (2008) we have a fairly good estimate of the shape of the initial power spectrum across the range of pitches explored by WMAP and other CMB experiments, and a less certain estimate outside this range. Amusingly, theoretical cosmologists are often more confident about the initial spectrum, since their theories predict a simple form almost identical to the one observed.
What is the primordial spectrum like? Is there a dominant pitch? Does it have harmonics? Is it musical? No – none of these. Nature is much too subtle to share our naive hopes. The primordial sound is pure noise. It contains all pitches with equal force. The spectrum is smooth and featureless, from the deepest notes to the highest. On reflection, this is how it should be: egalitarian through and through, since there had been nothing to favor one pitch over another. Because of this, structures of all size can now form – stars/galaxies/clusters/tapestry. By picking pure noise, Nature made by far the wisest and most creative choice.
To make an accurate sound, we must be more specific. The initial power spectrum seems to have a remarkably simple form: P(k) = Ak, where A is a constant, k is the frequency, and P(k) is the loudness at that frequency. A graph of this is shown in the next slide, together with its sound. It is a formless hiss spanning notes too low to hear and notes too high to hear. Although in this plot it appears to emphasize high pitches, in terms of the potential for forming structure, all pitches in fact have equal weight (hence the spectrum is said to be "scale invariant").
The figure also includes sound spectra for dark matter and atomic matter, taken around the time of the CMB. Clearly, the primordial spectrum generates quite different sounds as time goes by, for reasons we've already touched on. In a sense, we are witnessing the response of a complex resonator to a wide band stimulus. The primordial sound stimulates vibrations of all frequencies, but since the Universe is complex, some frequencies grow while others decay. As with any complex resonator, the final sound ultimately contains a full account both of the properties of the resonator and the history of the stimulus. Which is, of course, why Big Bang Acoustics provides so much information about the Universe.
A slightly different version of the primordial sound is given in the next below – this time shown in projected form, as it would appear on the CMB in the C(l) diagram.
C(l) at 300,000 yr