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Elegant Wiggles: Why the Universe Is Lumpy

Back in January the Edge posted almost 200 short essays in response to the question, "What is your favorite deep, elegant, or beautiful explanation?" Right away I knew what my favorite candidate would be: the prevailing explanation for why the universe is lumpy.
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Back in January the Edge (the website, not the guitarist) posted almost 200 short essays in response to the question, "What is your favorite deep, elegant, or beautiful explanation?"

Right away I knew what my favorite candidate would be: the prevailing explanation for why the universe is lumpy. The explanation combines two of the most interesting and consequential ideas of modern physics: Heisenberg's uncertainty principle from quantum theory, and the separate idea, stemming from Einstein's general relativity, that space and time are as malleable as a trampoline. Even better, the explanation for the lumps leads to predictions for specific features that should be observable in the universe today -- predictions that match the latest data so closely it's almost uncanny.

First the lumps. Why is matter and energy distributed so unevenly when we observe the universe on scales ranging from the human-sized to the supergalactic? Why, in other words, should there exist huge concentrations of stuff -- massive clusters of galaxies like the Virgo cluster, cosmic equivalents of New York City, teeming with energy and activity -- separated by vast expanses of emptiness, nearly devoid of any matter at all?

A partial explanation comes from gravity, the most aristocratic of nature's forces. Under gravity's inexorable tug, the rich really do get richer. A region of space that happened to have slightly more stuff than neighboring regions at early times would grow more rich in matter over time: any slight excess would attract more matter thanks to its greater-than-average gravitational pull. The matter that glommed onto the slightly-more-massive region, in turn, would leave the regions whence it came even more depleted. Over a cosmic history like ours, which stretches nearly 14 billion years, this slow, creeping accumulation can add up to the huge disparities we see today in the distribution of matter and energy across space.

But where did the initial unevenness come from? According to our best explanation to date, those miniscule, primordial bumps came from quantum theory.

Physicists describe matter and forces in terms of fields. All of space, for example, is pervaded by electromagnetic fields, responsible for making electric charges attract or repel. At the quantum-mechanical level, one can decompose these fields as collections of quanta, or tiny particles -- in the case of the electromagnetic field, the associated quanta are photons, individual particles of light. Even simpler types of fields can exist. For example, the Higgs particle, for which physicists are so avidly searching at the Large Hadron Collider, corresponds to a field with even simpler mathematical structure than the electromagnetic field.

The exact state of a quantum field at any instant of time shows characteristic wiggles: unavoidable fluctuations due to Heisenberg's uncertainty principle. At any given moment, at any given location, the energy distributed in matter will betray incredibly tiny, sub-microscopic fluctuations, whose expected behavior physicists can calculate. Though wispy and evanescent, these quantum fluctuations can also be measured in a laboratory. In fact, for certain systems the theoretical predictions and experimental measurements agree all the way out to 12 decimal places -- one part in a trillion -- likely the single most precise and well-tested aspect of modern science. (How physicists learned to master such tricky calculations is the subject of my first book, Drawing Theories Apart.)

Now for the second step. All those fields of matter, with their eensy-weensy quantum fluctuations, live in spacetime -- as far as we can tell, a spacetime governed by Einstein's general relativity. Among the most surprising lessons of relativity is that this seat of the action is also a player: Spacetime warps and distends in response to the presence of matter and energy. Plop a large, massive object like the Sun in some region of spacetime, and spacetime itself will deform.

Not only does spacetime deform in the large, like a trampoline bowing around a bowling ball tossed in its center, but spacetime can ripple, like tiny waves skittering across an otherwise smooth surface of a pond. Many types of gravitational waves are possible, including simple ("scalar") waves of spacetime distortion. Those gravitational wiggles are driven by the tiny quantum fluctuations of matter: Jiggle a field of matter here and you will generate tiny ripples in the fabric of spacetime.

But how could sub-microscopic quantum fluctuations, with characteristic height and wavelength smaller than the size of atoms, possibly account for galactic-sized agglomerations? The answer, again: gravity. More and more evidence suggests that at the earliest moments in our cosmic history, the universe underwent a period of explosive, exponential expansion known as "inflation." (For accessible introductions, see the opening section of this paper, or, even better, Max Tegmark's lovely essay.)

As space stretched by an enormous factor, perhaps 30 or more orders of magnitude (a 1 followed by 30 zeroes -- yeah, a lot), the wrinkles of spacetime got stretched, too. Quantum fluctuations of matter and their associated wiggles in spacetime, which had started out with wavelengths many times smaller than the size of an atomic nucleus, would get stretched to macroscopic, even galactic, size. The wiggles, in other words, would stretch long enough in space to account for galaxy-sized accumulations of matter.

Calculating the properties of these spacetime wiggles -- how the height or amplitude of the waves should vary with wavelength -- was once a cutting-edge endeavor. Nowadays advanced undergraduates can tackle the calculation, at least for relatively straightforward models. (This is an empirical statement, as I have learned from working with an outstanding group of physics undergraduates this year.)

The upshot: Inflation should have produced spacetime wiggles across a huge range of wavelengths, each with nearly the same height, yet not exactly the same height. The models predict a slight tilt: Longer-wavelength wiggles should have ever-so-slightly greater amplitude (or height) than shorter-wavelength wiggles. Cosmologists characterize such a tilt in terms of a "spectral index," n. A perfectly flat spectrum, in which wiggles of all wavelengths have the same height, corresponds to n = 1. Inflationary models typically predict n less than 1. Calculations for the simplest models yield 0.95 to 0.97.

What about the observations? Amazingly, cosmologists can study these primordial lumps to high precision, based on the pattern captured in the cosmic microwave background radiation, or CMB. The CMB is effectively a snapshot revealing how matter and energy were distributed throughout the universe at the moment of the photons' release, about 380,000 years after the big bang. Photons that hailed from regions of space that happened to have greater-than-average concentrations of matter had to expend more energy to escape the extra gravitational tug, and so appear to us today to have slightly less energy than photons that came from underdense regions. The difference is minute, about one part in a hundred thousand, yet measurable nonetheless. (My wife even bought me a CMB plushie, either for inspiration or to facilitate naps in the office.)

Using a variety of ground-based and satellite detectors, most prominently the Wilkinson Microwave Anisotropy Probe or WMAP satellite, cosmologists have measured the distribution of bumps and wiggles in the CMB. The latest observations indicate a measured tilt to the spectrum, with n = 0.968 +/- 0.012: nearly but not exactly flat, and an astounding match to the theoretical prediction.

Research continues. Some cosmologists still actively look for alternative explanations to inflation, though (to my knowledge) none has yet come close to accounting for the empirical data with this kind of precision. Meanwhile, other, subtle effects could be lurking in the CMB, which would indicate more complicated dynamics in the very early universe.

But let us pause and admire the audacity of this beautiful explanation, stemming from simple but important ideas. The universe is lumpy because matter must obey the uncertainty principle, and spacetime is jittery. Elegant wiggles, indeed.