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© UnknownIf gravity can sneak into dimensions that are closed to us, it might explain some puzzling cosmic anomalies

There is nothing certain in this world, US founding father Benjamin Franklin once wrote, except death and taxes. As a scientist, he might have added a third inescapable force: gravity, the unseen hand that keeps our feet on the ground.

Gravity is the universal force. Not only does it stop us getting above ourselves, it keeps Earth orbiting around the sun, our sun swinging around the centre of the Milky Way, the Milky Way in a merry dance around its neighbours, and so on upwards. It is actually the weakest of nature's four forces, but whereas the other three - electromagnetism and the strong and weak nuclear forces - unleash their full strength only at the scales of atoms and particles, gravity conserves its power to trump all comers in the cosmos at large. Just take any two things that have mass, and whatever their size, wherever they are, they will feel gravity's grasp in exactly the same way.

Or will they? Justin Khoury, now of the University of Pennsylvania in Philadelphia, and his colleagues Niayesh Afshordi and Ghazal Geshnizjani of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, are not so sure. They have listed a series of cosmological observations that cannot readily be explained with a one-size-fits-all gravity. None of these effects on its own, they stress, necessarily indicates anything amiss. But intriguingly, all of them melt away if you make just one assumption, albeit a controversial one: that how gravity works depends on the scale on which you look at it.

If right, the hunch has truly mind-boggling consequences. According to the theory, this variable gravity would be our first glimpse of spatial dimensions beyond our familiar three - dimensions infinitely large, but which remain forever closed off to us. Khoury acknowledges that it seems wacky. But as long as the observational anomalies are not explained, there is a feeling the idea should not be dismissed out of hand. "The work is credible, if a little optimistic," says David Spergel, an astrophysicist based at Princeton University. And intriguingly, the theory makes predictions we can test: so if hidden dimensions are there right under our noses, we should soon have the proof.

Gravity is a familiar, yet deeply perplexing force. Its story is bound up with two of the greatest names in physics, Isaac Newton and Albert Einstein. In 1687, Newton published his universal law of gravitation, which states that two objects feel an attractive force whose strength increases with their mass and decreases with the square of the distance between them: it scales as s-2 where s is the bodies' separation.

This searing intellectual insight embodied the motion of the planets, the flight of a cannonball and the dropping of an apple - all in one succinct formula. Yet Newton was hard pressed to explain the nature of a force that seem to be transported instantaneously, and with unerring accuracy, through empty space. It was only in 1915, with Einstein's general theory of relativity, that a halfway convincing answer was found.

According to general relativity, gravity arises because objects with mass or energy warp space and time around them, causing other objects to fall towards them. Working through the maths of the new theory, it became clear that Newton's universal inverse-square law needed tweaking when dealing with particularly massive or fast-moving bodies. With these modifications, we can predict gravity's effects from the smallest scales right up to the scale of the solar system with astounding accuracy.

So if the theory ain't broke, why try to fix it? The problem is that general relativity is incompatible with the later quantum theories that describe nature's other three forces. These theories say that forces are mediated by a constant exchange of particles; accordingly, gravity should be transmitted by a quantum particle known as a graviton. General relativity does not allow for such a possibility, and so physicists are left seeking a grander framework that will unite gravity and quantum theory into one "theory of everything".

And if you care to look on the very grandest cosmic scales, there is no shortage of niggling indications that something is not quite right with gravity. Take the cosmic background radiation, for instance. This consists of photons that have been speeding towards us from all sides since the big bang 13.7 billion years ago. On the way, these photons pass through great clusters of galaxies, gaining energy as they pass through them and losing it again as they come out the other end. Those two effects should cancel out.

Or at least they would do had dark energy not kicked in a few billion years ago. This form of repulsive gravity is the best explanation we have for why the universe's expansion seems to have started accelerating in recent aeons. One of its effects is to lessen the gravitational pull of a galaxy in the time it takes a photon to pass through it, so the photon exits without losing all the energy it gained on the way in. This means some background photons reaching us should be unexpectedly hot. That is indeed the case, but there's just one teensy problem: their energy gain is twice as large as we can explain using dark energy alone.

One theory fits all

A weaker gravity in those far-off distances and times when dark energy switched on would have been more easily and comprehensively overwhelmed by dark energy. "The effect would work hand in hand with dark energy to slow down the aggregation of matter," says Khoury. Photons passing through galaxies would be relatively even hotter, causing the discrepancy to melt away.

Then there is the mystery of "dark flow", which has emerged from surveys of thousands upon thousands of distant galaxies. The overall expansion of the universe means that most of these galaxies are travelling away from us. But once this effect is taken into account, their velocities should be determined by local gravity conditions and in a large enough volume of space should cancel out.

Unfortunately, they don't. Over middling scales of a few hundred million light years, galaxies look as if they are flowing towards a giant central concentration of mass - one so large that it could not possibly have gathered since the big bang. It has been proposed as a first glimpse of what lies beyond the horizon of the visible universe (New Scientist, 24 January, p 50), but if gravity is stronger at these scales the need for such exotic explanations disappears. "Not only would stronger gravity aggregate matter more quickly, but galaxies would fall towards the enhanced matter concentrations faster," says Khoury.

And then there's the Lyman-alpha forest. Liberally dabbed across the cosmos are tenuous clouds of hydrogen gas, the precursors of galaxies. These absorb light at a wavelength of 122 nanometres, creating a distinctive dip in the spectrum of light penetrating through them known as the Lyman-alpha line. That's if they are stationary, but in fact different clouds are moving at different speeds towards or away from us because of the universe's variable expansion over time. These clouds will absorb light at varying wavelengths owing to the Doppler effect, and light arriving at Earth from distant sources will have many bites taken out of it. From this forest of spectral lines astronomers can deduce the distribution of hydrogen clouds in space. Like the dark-flowing galaxies, they seem more closely clumped together on middling scales than standard cosmology can explain - again, just as if gravity had once been a stronger force binding them together.

But hold on a moment. Cosmic background photons suggest weaker gravity on one scale; dark flow and the Lyman-alpha forest imply stronger gravity on another. Surely one theory cannot explain both? Remarkably, that is just what Khoury and his colleagues are claiming.

The context of their work is an outgrowth of string theory - the currently favoured route to a theory of everything - known as brane theory. String theory treats the particles that make up matter and transmit forces as tiny one-dimensional strings of mass-energy vibrating in a space-time of 10 dimensions, known as the bulk. Brane theory goes even further, describing our universe as a "3-brane", an object with three dimensions of space and one of time adrift in the bulk. In this scenario, vibrating string-particles are anchored firmly to the brane. All of them except gravitons, that is. Gravitons are vibrating loops of string with no free ends to fix to the brane - so they can leak off into the bulk. This leakage explains why gravity is intrinsically so much weaker than the other fundamental forces.

Infinite dimension

It could also account for the relatively weaker gravity that the cosmic background photons seem to have experienced. The context is a set of brane-world theories known as Dvali-Gabadadze-Porrati (DGP) models after the three theorists at New York University who suggested them in 2000. These propose the existence of at least one off-brane dimension that is infinite in size.

With one such extra dimension, gravity does not scale with separation as s-2, but as s-3 - so if two objects double the distance they are apart, their mutual gravity is not four times, but eight times weaker. With two dimensions, the fall-off is s-4, with three s-5 and so on. Khoury and his colleagues' calculations show how a DGP model with two or more extra dimensions would be just the ticket for reproducing the gravitational properties of the universe as we see them.

There is an obvious question: how come we don't perceive these extra dimensions? If more than three dimensions of space exist, why do our senses persist in limiting us to three? Standard string theories get around this embarrassment by postulating that the extra dimensions are rolled up to scales enormously smaller than an atom, so we simply do not notice them. Brane models are more brazen. You and I do not see the infinitely sized extra dimensions because we are made up of ordinary particles of matter that are firmly pinned to the brane. If we wish to emulate Alice and clamber through the looking glass to roam the extra dimensions beyond, our only chance is to reconstitute ourselves from gravitons - the only truly free particles.

There's still a pressing objection. If these extra dimensions really do exist, why do we experience gravity as we do, as an s law? Again, the theory supplies an answer. A mass sitting on the brane - embedded in our universe - radiates gravitons in all directions, both along the brane and into the bulk. But the brane is a stiff medium, so they propagate far more readily along the brane than away from it, rather as the reverberations when you tap a metal sheet travel along the sheet more easily than they do into the surrounding air. If you're anywhere close to a massive object - as we are in our solar system - the gravity you feel will therefore be hugely dominated by the on-brane, s-2 gravity.

The further away you are from a source of gravity, though, the more this force drops off. At very large cosmic scales, where the average density of matter is much smaller than in our neighbourhoood, the weakening through graviton leakage becomes proportionately more significant, and the gravity felt on the brane begins to diverge noticeably from the s-2 law.

So the effect of hidden dimensions might nicely explain the weaker gravity demanded by the cosmic background photons for the largest scales. But what of the stronger gravity on intermediate scales indicated by dark flow and the Lyman-alpha forest? That, says the theory, is all down to the peculiar behaviour of gravitons immediately they leak off the brane into the bulk. Without the stiff sheet of the brane to propagate through, they slow down, in effect acquiring a mass.

Any particle with mass by definition feels gravity. So the off-brane gravitons start gravitating: at small scales close to the source of mass, where there are lots of them confined in a small space, exclusively with each other, but as they spread out further into the bulk also with matter on the brane. The result is a strengthening on intermediate scales of the on-brane gravity predicted by the Newtonian inverse-square law by about a third. At the very largest cosmic scales, however, the gravitons in the bulk are sufficiently dispersed that this strengthening is overwhelmed by the much larger weakening effect caused by the initial leakage.

So there it is: a theory that can explain both anomalously weak and anomalously strong gravity. Is it going to tie up all the loose ends of the current cosmology? Perhaps, says Jim Peebles of Princeton University. "It is a kludge," he says - something that by rights should not work, but might just. "I won't be ignoring the idea, but I wouldn't bet the farm on it, either."

The most significant objection is that none of the anomalous effects that Khoury and his colleagues set out to explain is on its own particularly significant. With more and better data, they might disappear of their own accord - or might not. "A sequence of small pieces of evidence taken together can be a strong indication of new physics, perhaps very close to what this group has described," says Glenn Starkman of Case Western Reserve University in Cleveland, Ohio. "The challenge is to improve the observations," says Khoury. "If the anomalies don't go away, we will be on safer ground."

There might be other, more immediate tests. According to general relativity, light and matter feel gravity in the same way: they both follow the same paths around massive objects dictated by their warping of space-time. But any pure theory of gravity such as Khoury's variable gravity affects only matter. So proving the existence of hidden dimensions could be as simple as observing the bending - "gravitational lensing" - of light from a distant source as it passes by a galaxy cluster on its way to Earth, and so inferring the cluster's mass. If we can then measure the cluster's gravitational pull on a second cluster - for instance, by how fast it is dragging the second cluster towards it - we can acquire a second, independent mass estimate.

If hidden dimensions are modifying gravity, the two estimates will be different by 20 to 30 per cent, says Khoury. Current galaxy cluster measurements are not quite accurate enough to pinpoint an effect of this size, but the current generation of surveys should deliver a definitive answer within the next 10 years.

Even if we do get proof that other dimensions exist we would be a way away from ever entering them. Still, it would be a dumbfounding indication of how even the stuff we are made of deceives us in our perceptions of the universe.

It's all a far cry from that day on a farm in 17th-century Lincolnshire when, in the apocryphal scene beloved of cartoonists, a falling apple knocked the idea of universal gravitation into Newton's head. Khoury is banking on what applies to apples also holding for Newton's theory: what goes up must - eventually - come down.