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According to Pietronero, there simply hasn't been enough time since the universe came into being 14 billion years ago for gravity to sculpt structures larger than about 30 million light years across: expansion would
have prevented anything larger from forming. "The existence of structures much larger than this implies a crisis of the present view of structure formation," he says. This present view is the "cold dark matter model", in which the glowing masses of stars and galaxies are only the tip of the cosmic iceberg. Luminous matter makes up roughly 15 per cent of all the matter in the universe
- the other 85 per cent is mysterious dark matter.
Hogg's team says that the new observations do not undermine the standard view as Pietronero claims. Instead, they maintain that the cold dark matter model explains the Sloan data quite accurately. For that to be
true, however, Hogg's team have to put a number called a bias parameter into their equations. It reflects the difference between the distribution of matter in computer simulations of the cold dark matter model and the
observed distribution of luminous matter. Collisions between particles of ordinary matter help it clump together, but dark matter is thought not to behave in the same way. That suggests it could be spread out in space more evenly than ordinary matter, so cosmologists assume that the distribution of the matter we can see - galaxies, say - is not a true reflection of the distribution of all the matter that is out there. They believe the structure of the universe is really much "smoother" than it appears to be, because dark matter dominates. In the case of the Sloan survey, the bias is 2: the visible galaxies are clumped twice as densely as the predicted total distribution of matter in the universe.
Sylos Labini, however, sees the bias as a fudge that allows cosmologists to discount the observed clustering of galaxies and to assume that the gigantic clusters of superclusters are only half the problem they appear to be. "The bias is a way to hide the size of structures behind some ad hoc parameter," he says. Mainstream cosmologists, however, feel the bias is justified, assuming that galaxies cluster in regions of space that are replete with excess dark matter. According to the standard model, dark matter is everywhere, but galaxies only shine in the rare regions where dark matter is densest. Dark matter also lingers in the voids where no light shines but here it is thinly spread out. In other words, while the luminous galaxies look very clustered, the underlying blanket of dark matter is far smoother, supporting the claim of homogeneity. "If the cold dark matter model is correct, then there should be dark matter in the voids," Hogg says. The million-dollar question is: what is the real distribution of dark matter? Is dark matter smooth or fractal? Is it clustered like the galaxies, or does it spread out, unseen, into the great voids? If the voids are full of dark matter, then the apparent fractal distribution of luminous matter becomes rather insignificant. But if the voids are truly empty, the fractal claim requires a closer look. Astronomers are now providing our first glimpse into the voids and our first look at the pattern of invisible matter. Richard Massey of the California Institute of Technology in Pasadena and others in the Cosmic Evolution Survey project have just created the first 3D map of dark matter in the universe (New Scientist, 13 January, p 5). They were able to find the dark matter by observing its gravitational effect on any light streaming past it. Combining data from the Hubble Space Telescope, the Subaru telescope in Hawaii and the Very Large Telescope in Chile, they mapped the distribution of dark matter at scales ranging from 23 million to 200 million light years across.
Massey's team found that the dark matter distribution is nearly identical to the luminous matter distribution. "The first thing that strikes me is the voids," Massey says. "Vast expanses of space are completely empty.
The dark matter makes up a criss-crossing network of strings and sheets around these voids. And all the luminous matter lies within the densest regions of dark matter." Although this distribution of dark matter seems to favour the idea that the universe is fractal, Hogg isn't convinced. "It is interesting," he says, "but measurements of dark matter are much less precise than measurements of galaxy distributions."
"The result is very new," Massey agrees. "It demonstrates a very exciting new way of looking directly at dark matter and will be vital in future work, but hasn't yet been subject to all the analysis that has been applied to galaxy surveys." When asked if the dark matter exhibits an explicitly fractal structure, Massey replies, "We don't know yet." "The universe is not a fractal," Hogg insists, "and if it were a fractal it would create many more problems that we currently have." A universe patterned by fractals would throw all of cosmology out the window. Einstein's cosmic equations would be tossed first, with the big bang and the expansion of the universe following closely behind.
Hogg's team feel that until there's a theory to explain why the galaxy clustering is fractal, there's no point in taking it seriously. "My view is that there's no reason to even contemplate a fractal structure for the universe until there is a physical fractal model," says Hogg. "Until there's an inhomogeneous fractal model to test, it's like tilting at windmills." Pietronero is equally insistent. "This is fact," he says. "It's not a theory." He says he is interested only in what he sees in the data and argues that the galaxies are fractal regardless of whether someone can explain why. As it turns out, there is one model that may be able to explain a fractal universe. The work of a little-known French astrophysicist named Laurent Nottale, the theory is called "scale relativity" (see "Fractured spacetime"). According to Nottale, the distribution of matter in the universe is fractal because space-time itself is fractal. It is a theory on the fringe, but if the universe does turn out to be fractal, more people might sit up and take notice.
A resolution to the fractal debate will only come with more data. Sloan is currently charting more galaxies and will release a new map in the middle of 2008. According to Sylos Labini, this will cover over 650 million light
years and should tell us if the apparent transition to homogeneity extends beyond 200 million light years. For now, the pattern of the world, imprinted at the origin of the universe, remains a secret glimpsed only in the
knowing shimmer of the stars.
Fractured space-time
French astrophysicist Laurent Nottale has developed a theory that takes fractals to a whole new level. A researcher at the Meudon Observatory in Paris, Nottale set out to extend Einstein's principle of relativity -
in which the laws of physics remain the same regardless of the motion of an observer - to a theory in which the laws of physics would remain the same regardless of the scale at which the universe is being
observed. He found that the underlying space-time of such a theory would have to be fractal. In Nottale's theory, called scale relativity, the underlying fractality of space-time is most noticeable in the
quantum world. Quantum behaviour, he claims, can be understood geometrically - particles move along fractal trajectories. On large scales, his model could explain a fractal pattern of the galaxies.
The most profound question in physics today is how to unify the really small with the really big - and when it comes to matters of scale, fractals may turn out to be a key ingredient.
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