Is the universe a fractal?

10 March 2007 - From New Scientist Magazine by * Amanda Gefter
(Illustration at top here)
WRITTEN across the sky is a secret, a hidden blueprint detailing the original design of the universe itself. The spread of matter throughout space follows a pattern laid out at the beginning of time and scaled up to incredible proportions by nearly 14 billion years of cosmic expansion. Today that pattern is gradually being decoded by analysing maps of the distribution of the stars, and what has been uncovered could shake modern cosmology to its foundations.

Cosmology is founded on the assumption that when you look at the universe at the vastest scales, matter is spread more or less evenly throughout space. Cosmologists call this a "smooth" structure. But a small band of researchers, led by statistical physicist Luciano Pietronero of the University of Rome and the Institute of Complex Systems, Italy, argues that this assumption is at odds with what we can see. Instead they claim that the galaxies form a structure that isn't smooth at all: some parts of it have lots of matter, others don't, but the matter always falls into the same patterns, in large and small versions, at whatever scale you look. In other words, the universe is fractal.

It is a controversial view, and one that sparked an intense debate over a decade ago. Since then, astronomers have surveyed ever-greater numbers of galaxies, taking larger and larger samples of the universe. Now the biggest galaxy survey ever and a brand new map of the universe's dark matter are adding fuel to the fire.

At stake is far more than the way galaxies cluster. A fractal universe could undermine cosmology's most basic assumptions. "All of the observations we make depend to a greater or lesser extent on the idea that the universe is homogeneous," says David Hogg of New York University, who leads a team of physicists that disputes Pietronero's view.

This idea that matter is spread more or less evenly throughout the universe is embodied in Einstein's cosmological principle. Einstein formulated it after publishing his general theory of relativity, which describes how the distribution of mass bends space-time and creates gravity. It allows cosmologists to use the equations of general relativity to describe the geometry of the whole universe. As a result it has led to a picture of a universe expanding uniformly from the big bang and in which cosmological measurements have defined meanings.

Fractals allow Pietronero to paint a very different sort of picture - one in which the irregular distribution of matter that we see around us never evens out into a smooth structure, but repeats itself at ever grander scales. Fractals are familiar enough: we see them in the branching of trees, the curves of coastlines, lungs, turbulence and clouds. No matter what scale you look at them, fractal patterns look the same. Think of broccoli: a tiny branch looks much the same as the whole vegetable. Zoom in or zoom out, the structure looks the same - exquisitely detailed, never smooth. Fractals can be beautiful to look at, but when it comes to galaxies it may be a subversive kind of beauty.
(Insert from Dan - Fractality at Universal scale is as necessary as at biologic scales - only that produces GRAVITY and SENTIENCE)

Certainly the universe does not look smooth. Some regions contain clusters of matter; others are virtually empty. Hundreds of billions of stars group together to form galaxies, and galaxies congregate in clusters. Clusters assemble into colossal structures called superclusters that can stretch out for 100 million light years and look uncannily like fractal patterns (see Diagram).

Even superclusters string together in long filaments and sheets that stretch like ghostly cobwebs across an otherwise empty sky. The Sloan Great Wall, for example, which was discovered in 2003, spans more than a billion light years. These filaments and sheets seem to encircle huge voids of empty space. The voids range from 100 to 400 million light years in diameter, making the whole assemblage appear as an immense, glowing lattice punctuated by wells of darkness.

No one disputes that the universe is far from smooth on relatively small scales - by which cosmologists mean thousands of light years. But Hogg's team is convinced that if you zoom further out, smoothness reigns. "When you're looking at the size scales of galaxies, groups of galaxies, clusters, superclusters and filaments, it looks like a fractal," says Hogg. "But once you get larger than all of that, then it starts to look homogeneous."
“Galaxies, groups of galaxies, clusters and superclusters all appear fractal, but at larger scales the cosmos is smooth”

What has convinced him is his team's analysis of the latest data from the Sloan Digital Sky Survey, the largest 3D map of the galactic universe so far. His team insists that the map is proof of smoothness. The fractal camp, however, are sceptical. In fact, they say the Sloan observations confirm what they've been claiming all along.

It might appear to be deadlock, but at least with the Sloan survey the two sides can agree what they're disagreeing about. For years Pietronero and his team argued that the statistical methods mainstream cosmologists were using to establish homogeneity were flawed because they start off by assuming that matter is evenly spread. The team was mostly ignored until 2004, when Hogg and astrophysicist Daniel Eisenstein of the University of Arizona in Tucson spent a summer in Paris with Pietronero's colleagues, cosmologists Francesco Sylos Labini of the Enrico Fermi Centre and the Institute for Complex Systems, Rome, and Michael Joyce of the Pierre and Marie Curie University, Paris.

"We argued every day about fractals," Hogg says. "Those battles raged over lunch and coffee and finally convinced us by the end of our visit that we should be doing the analysis as they say."

When they returned to the US, Hogg and Eisenstein applied the fractal team's methods to a sample of 55,000 luminous red galaxies mapped by Sloan. They found that the galaxies do form a fractal pattern, but as they looked at bigger and bigger scales, the pattern appeared to disintegrate and smooth out at just over 200 million light years - a scale far larger than most cosmologists had expected.

But Pietronero and Sylos Labini are not convinced. Instead, they believe that if astronomers could continue to zoom out and look at even larger scales, they would find more clustering. They suspect that the apparent smoothness at 200 million light years is not real, but rather an illusion created by statistical effects due to the limited range of the Sloan survey.

Hogg's team, though, insist that their evidence of homogeneity is statistically significant. "I think the result really is secure," says Hogg. "I would stake my scientific reputation on that."

Even if the result is real, mainstream cosmologists still have a huge problem on their hands. The fact that the fractal patterning extends to far bigger scales than anyone had expected means that there must be far bigger structures than anyone expected - structures that are even bigger than superclusters. The fractal team argues that the standard model cannot explain the existence of these galactic giants. "If you look at the galaxy data, you can see enormous objects hundreds of millions of light years across, stuff that's really huge," says Pietronero. "This is a huge problem. You're going to have to change the story very radically."

The usual story runs something like this. In the tiny fluctuations of the nascent universe, matter began to collect in denser regions, setting off a chain reaction of gravitational collapse that has given us the large-scale structure we see today. Gravity has worked from the bottom up, building galaxies first, then collecting galaxies into clusters, then clusters into superclusters and so forth. But while the matter has been clumping together, the universe has been expanding, and thus a battle has ensued: gravity versus expansion.

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.
“Einstein's equations would be tossed out first, followed by the big bang and expansion of the universe”

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 space-time"). 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.
From issue 2594 of New Scientist magazine, 10 March 2007, page 30-33
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.
Discovery of Cosmic Fractals by Yurij Baryshev and Pekka Teerikorpi

* 25 January 2003
* NewScientist.com news service
* Marcus Chown

Discovery of Cosmic Fractals by Yurij Baryshev and Pekka Teerikorpi, World Scientific, $38/£26, ISBN 9810248725 Reviewed by Marcus Chown

FRACTAL structures are everywhere - in clouds, in snowflakes, even in Islamic art, says Benoît Mandelbrot, godfather of fractals. So why not throughout the Universe? Why not indeed?

In Discovery Of Cosmic Fractals, astronomers Yurij Baryshev and Pekka Teerikorpi set out the evidence for fractal structures everywhere from interstellar clouds to galactic dark-matter haloes. Intriguingly, they say, a fractal distribution of matter can squirrel away "baryonic dark matter" (which consists of familiar particles such as neutrons and protons, rather than exotic ones) in small molecular clouds that might so far have escaped detection. But the most controversial idea by far is that the entire Universe is fractal.

Recall that Einstein's fiendishly complex equations of gravity can be solved exactly only if we assume that the Universe on the large-scale is homogeneous - that is, it looks the same from every place. (Dan insert: Einstein's OTHER problems..........) This assumption, enshrined in the cosmological principle, leads to the Friedman-Robertson-Walker solutions, the big bang models. Abandon that assumption and everything we thought we knew about the Universe gets jettisoned, as New Scientist has pointed out (21 August 1999, p 22).

No one can deny that the galaxy distribution is fractal in our cosmic neighbourhood. The "geometry of chaos" is apparent from scales of about 300,000 light years up to at least 300 million light years. But what about beyond? Here lies the battleground.

While mainstream astronomical opinion maintains that galaxy surveys probing even farther out into the Universe will reveal the fractal distribution giving way to homogeneity, a vocal minority led by Luciano Pietronero of the University of Rome claim the Universe will be found to be as self-similar as a snowflake on all observable scales.

Mandelbrot, who has written the introduction to this book, has even proposed the conditional cosmological Principle, which states that the Universe looks the same from all locations, provided they contain a galaxy and not a void. This subtle variation on the Cosmological Principle implies a profoundly different cosmology from the standard one.

Mandelbrot and Pietronero face many problems. They must somehow extract cosmological solutions from Einstein's equations. And they must also explain the Hubble law that states that the recession velocity of galaxies is proportional to their distances. In the standard picture of the Universe, this is natural if the Universe expands and remains uniform.

This is a stimulating book, more than half of which stands alone as a first-rate historical primer on astronomy and cosmology. It is a bold and controversial claim indeed that the fractal structure of the Universe is a key cosmological discovery to stand alongside Hubble's discovery of the expanding Universe, and Penzias and Wilson's of the "afterglow" of the big bang. Time alone will tell whether it is a claim too far.
From issue 2379 of New Scientist magazine, 25 January 2003, page 52

WHEN cosmologists speculate on the nature of the Universe, they make an unspoken assumption-that matter is spread uniformly throughout space. Yet when astronomers peer out across the Universe they see something very different. Galaxies are gathered together in great chains and walls which snake around vast regions of empty space called voids. The Universe appears anything but uniform.

"Yes, there does appear to be a contradiction," admits Ofer Lahav of the Hebrew University in Jerusalem and the Institute of Astronomy in Cambridge. But Lahav contends that the Universe, though undeniably clumpy on the small scale, becomes smooth on the largest scales. "I like to think of it as an ocean, which looks choppy on the scale of individual waves but from far above, on scale of tens of kilometres, is perfectly smooth," he says.

Lahav's is very much the conventional view. "I would say that more than 95 per cent of astronomers believe the Universe is uniform on the very large scale," says Peter Coles, professor of astrophysics at the University of Nottingham. But an opposing opinion is now causing a stir. A maverick group based in Europe has suggested that the Universe never becomes smoothed out, even on the largest scales. "My contention is that it is clumpy on all the scales so far explored," says Francesco Sylos Labini, an astronomer at the University of Geneva. "In fact, studies we have done show that the distribution of matter is fractal, just like a tree or a cloud."

If this dissenting view is correct and the Universe doesn't become smoothed out on the very largest scales, the consequences for cosmology are profound. "We're lost," says Coles. "The foundations of the big bang models would crumble away. We'd be left with no explanation for the big bang, or galaxy formation, or the distribution of galaxies in the Universe."

The standard models for describing the big bang and the evolution of the Universe are called Friedmann-Robertson-Walker (FRW) models. Their starting point was general relativity, the theory of gravity published by Einstein in 1915. In 1922, following Einstein's lead, the Russian physicist Aleksandr Friedmann applied general relativity to the whole Universe. (His equations were later recast by the American cosmologist Howard Robertson and Briton Arthur Walker). It was Einstein and Friedmann who first made the assumption that the Universe is both homogeneous-the same in all places-and isotropic-the same in all directions. This is known as the Cosmological Principle.

There were two reasons for making such an assumption. The first was purely practical: Einstein's complex equations are extremely difficult to solve for a Universe that is not smooth. The second reflected a scarcity of observations of the Universe. "Nobody knew anything about the large-scale structure of the Universe-galaxies weren't even generally accepted as the building blocks of the cosmos," says Lahav. "The simplest thing in the circumstances was to apply Ockham's razor and assume a homogeneous and isotropic Universe."

For most of this century, this assumption has been impossible to prove observationally. But now astronomers have begun to observe a big enough chunk of the Universe to at last put it to the test. In the 1980s, two of the most important galaxy surveys were the CfA red shift survey, carried out by Margaret Geller and John Huchra of Harvard-Smithsonian Center for Astrophysics, and the IRAS red shift survey carried out using NASA's Infrared Astronomical Satellite. Both probed out to about 300 million light years-or, to put it another way, they looked back to a time when the Universe was about 95 per cent of its present age.

There is no doubt that on this relatively small scale, the Universe is far from homogeneous. Most astronomers talk of "hierarchical clustering"-galaxies clumping together into clusters and clusters into superclusters. One commonly used measure of homogeneity is the "two-point correlation function". This is the probability of observing a galaxy at a certain distance from a chosen galaxy compared with the probability of finding one at the same distance if galaxies are spread uniformly throughout space. It turns out that you are twice as likely to find a galaxy at 15 million light years from a given galaxy in the real Universe as in a uniform Universe.

However, according to Lahav and his Cambridge colleagues Kelvin Wu and Martin Rees, this measure gradually declines towards 1 as scale increases. They estimate that the Universe becomes nearly homogeneous on scales larger than about 900 million light years-looking back to when the Universe was about 85 per cent of its present age. "On the largest scales we have probed, the Universe appears to become perfectly smooth," says Lahav.
Fractal dimension

But the mavericks, led by Lucian Pietronero of the University of Rome, dispute this. Having analysed the same galaxy surveys as everyone else, they claim that hierarchical clustering continues through to the very largest scales. This property, of similar patterns recurring at every scale, is a defining characteristic of fractals (see Diagram). "Our tests show that the Universe never becomes homogeneous in the available galaxy samples," says Sylos Labini, who began his work while in Pietronero's team. "It remains hierarchically clustered. It remains fractal."

The team maintains that orthodox cosmologists are mistaken. "What they are seeing is an artefact of the way they analyse galaxy surveys," says Sylos Labini. In conventional calculations of how close to homogeneity the Universe is-the two-point correlation function, for example-astronomers look for departures from the average density of the Universe. This necessarily assumes that there is such a thing as average density (see Diagrams) (here). "If the Universe is fractal, however, it has no characteristic scale," says Sylos Labini. "Everything, including the average density, changes with scale so the concept is meaningless. It's not surprising that people find the Universe is homogeneous when homogeneity is one of their basic assumptions."

To avoid this, Pietronero and his team calculate the extent of galaxy clustering by using statistical methods that take account of the properties of fractals. The simplest technique is to measure the number of neighbours around a chosen galaxy within a radius R. In fractal maths, this number is proportional to RD, where D, the fractal dimension, can have any value between 0 and 3. When D is 3, galaxies are distributed evenly within a sphere-the conventional view. But when D is not a whole number-fractal, that is-the galaxies cease to be distributed evenly.

From their measurements, Pietronero and his colleagues estimate that D is about 2.1, implying that the Universe is fractal on scales up to 300 million light years. There is a proviso, however. "We should not forget the invisible `dark' matter, which is thought to account for at least 90 per cent of the mass in the Universe," says Sylos Labini.

If the voids we see, apparently empty of galaxies, are in fact full of dark matter, then the Universe may still be homogeneous and FRW models will apply. "However, it seems very unlikely that the clustering of ordinary light-emitting matter and dark matter would be completely different," says Sylos Labini. If, on the other hand, the voids are empty of dark matter and the distribution of dark matter is roughly the same as that of ordinary matter, then the Universe is even more inhomogeneous than the luminous matter indicates.

Of crucial importance, then, are observations that are sensitive to the distribution of all matter rather than merely the distribution of luminous matter, which is what the galaxy surveys provide. One such probe is provided by the "streaming motions" of galaxies. As well as taking part in the continuing expansion of the Universe, some galaxies are also attracted by the gravity of unseen concentrations of mass, and move towards them. From this streaming motion, astronomers can deduce the total amount of matter pulling them through space.
Invisible mass

Another mass probe is provided by galaxies whose light is distorted, or "gravitationally lensed", by the gravity of matter close to the path it takes on its journey to Earth. "The indications so far are that the visible mass in the Universe roughly traces out the invisible mass," says Lahav. So dark matter does not bolster Sylos Labini's contention that the Universe is fractal (or, for that matter, Lahav's that the Universe is fractal on small scales and homogeneous on larger ones.)

But just suppose the Universe were fractal. Would it be the catastrophe that theorists claim? Would it mean abandoning the existing cosmological models? "Yes," says Sylos Labini. "The usual FRW models all assume a Universe with a constant matter density."

One way we could obtain solutions to Einstein's equations for a nonuniform Universe would be to assume that the inhomogeneity is simply a small "perturbation" on a homogeneous Universe. But this won't work for a fractal Universe, because it is more than a mere perturbation-it is radically different. The problem with a fractal is that it cannot even be described at each point in space by the formulas that conventional theory uses. "It is impossible to solve Einstein's equations exactly for a fractal distribution of matter," says Sylos Labini.

Despite this formidable theoretical challenges, Sylos Labini believes a fractal Universe is more exciting than a homogeneous one. "We are facing a new and challenging problem which we are a long way from solving," he says. "For some questions, the fractal structure leads to a radically new perspective and this is hard to accept. But it is based on the best data and analyses available. It is neither a conjecture nor a model-it is a fact."

Few would go anything like as far as this, though Coles admits that galaxy surveys as yet provide only weak evidence that matter is distributed smoothly throughout the Universe. "Existing galaxy surveys sample too small a volume to show the scale of homogeneity," he says.

But Lahav and his colleagues do not rely solely on galaxy surveys to support their case that the Universe is ultimately homogeneous. They bolster it with other evidence, such as the cosmic background radiation, the microwave "afterglow" of the big bang which still fills the Universe 15 billion years after the event. Since this radiation comes from an era within a mere 300 000 years of the birth of the Universe, it gives a look-back time close to 0 per cent the age of the Universe.

In 1991, NASA's Cosmic Background Explorer satellite (COBE) discovered that the temperature of the background radiation varies by less than 1 part in 100 000 from one direction in the sky to another. Since the radiation was in intimate contact with matter at the time, this allows astronomers to estimate the smoothness of matter at the beginning of the Universe. "We're talking about no variations bigger than 1 part in 100 000," says Lahav. "So, on the biggest scales possible, the Universe is almost completely smooth."

Not unexpectedly, Sylos Labini sees things differently. He questions the wisdom of jumping straight from the distribution of radiation seen by COBE to that of matter. "Inferring the distribution of matter from the distribution of radiation requires a complex theory with many assumptions," he says. "We should be very cautious."

On the other hand, Lahav points out that Sylos Labini and his colleagues have trouble explaining why there should be a fractal distribution of matter in the Universe. "There is no dynamical theory to explain how such a fractal Universe could have arisen from the pretty smooth initial state we know existed in the big bang," says Lahav.

"Yes, that's true," admits Sylos Labini. "It's a very difficult problem: how does gravity turn an initially smooth distribution of matter to a fractal one?" But just because something is hard to explain has nothing to do with whether it is true or not. "Facing a hard problem is far more interesting than hiding it under the rug by an inconsistent procedure," he says.

(Insert here from DAN - wait til the fools discover fractality IS the cause of GRAVITY!!!!!!!!! Hope they are at least embarassed.)

By contrast, Lahav says his picture is easier to explain. "The transition from hierarchical clustering to homogeneity is completely compatible with the accepted ideas of galaxy formation," he says. In the conventional picture, the Universe starts off with tiny density fluctuations-ripples in an otherwise smooth distribution of matter. Nobody knows for sure how these came about but a fair bet is that they were impressed on the Universe by quantum processes in the first split second of its existence. These are then amplified by gravity: denser regions of the Universe have stronger gravity, so they pull in more matter, making them more dense, and so on. "It's like capitalism," says Lahav. "The rich get richer and the poor poorer."

However, this process must also take account of the fact that the Universe is expanding and this expansion tries to pull apart material that is trying to clump. On the small scale gravity wins and material clumps into galaxies and clusters-and even superclusters. But the expansion gets bigger as the scale increases. This is the famous Hubble law, which says that the velocity of recession of two galaxies increases in step with their separation. Inevitably, then, there is a scale at which the expansion overwhelms gravity and no more structures can form. "This is where we see the transition to homogeneity," says Lahav.

There is clearly a huge gap between a look-back time of 95 per cent for the galaxy surveys and a look-back time of close to 0 per cent for the big bang radiation. Lahav goes as far as calling the region in between an "observational desert". Until cosmologists find oases in this desert, the debate over whether the Universe is homogeneous will not be resolved.

At least one such oasis does exist, and Lahav and his colleagues have recently visited it. This is the cosmic X-ray background, a universal glow of X-rays that was discovered in 1962 and is thought to be the total of all emissions from "active galaxies" such as distant quasars. Lahav believes their average distance is as much as 1800 million light years, which corresponds to a look-back time of about 12 per cent of the age of the Universe. "The evidence from the X-ray background is that the Universe is smooth on such large scales," says Lahav. Coles agrees. "I'm 99 per cent sure the Universe is homogeneous," he says.

Of course, Sylos Labini has a different interpretation. "I make the same argument as for the cosmic background radiation," he says. "A fractal distribution of active galaxies will appear isotropic on average-but this does not imply homogeneity."

Galaxy surveys that see farther out across the Universe are crucial for filling the gap, and two are already under way. The American-Japanese Sloan Digital Sky Survey, which uses a purpose-built telescope in New Mexico, should observe a total of 1 million galaxies over a quarter of the sky. And the Anglo-Australian Two-Degree Field, or 2dF, survey has already measured the red shift of more than 40 000 galaxies, and aims to measure 250 000. Both surveys will probe to a look-back time of 85 per cent of the age of the Universe.

Astronomers are also trying to observe variations in the temperature of the cosmic microwave background radiation between parts of the sky that are 1 degree apart or less. These correspond to regions of the Universe smaller than were probed by COBE but still much larger than the biggest galaxy surveys. So while the galaxy surveys push into the desert from one direction, the cosmic background experiments are coming in from the other. "When they meet in the middle, the argument will be over," says Lahav.
From issue 2200 of New Scientist magazine, 21 August 1999, page 22