Published online 23 February 2011 | Nature | doi:10.1038/news.2011.105

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A model of the cosmological constant invokes alternate realities.

Theorists have struggled to reconcile the observed expansion of the Universe with the predictions of quantum field theories. NASA, ESA, and the Hubble Heritage Team

Our limited view of the cosmos obscures the identity of the mysterious forces that are responsible for the accelerating expansion of the Universe. Physicists at the University of Cambridge, UK, now say in two papers that the 'cosmological constant' — which is used to represent the Universe's expansion in cosmological equations — depends on the time and location where it is measured. This could explain long-standing problems with the constant and help physicists to explain the Universe's expansion.

The most convenient explanation for the observed expansion is that empty space has a 'vacuum energy' that generates the force necessary to push matter apart. It is this energy that the cosmological constant accounts for in equations. But physicists have struggled to reconcile the observed expansion with their theoretical explanations.

One difficulty, for example, is the mismatch between the observed expansion and the predictions of many quantum field theories. These predict that pairs of quantum mechanical particles constantly popping out of the vacuum and disappearing again produce a repulsive force — known as quantum vacuum repulsion — that is at least 1056 times larger than the cosmological constant. Any theory accounting for the expansion would not only need to predict the constant correctly, but also cancel out the huge expansion predicted by such theories.

A second difficulty is that when the cosmological constant is expressed in units of time, it is equivalent to 9.7 billion years — surprisingly similar to the age of the Universe, which is about 13.7 billion years old. Physicists have long been puzzled by this 'coincidence problem' of two supposedly unrelated numbers being roughly the same.

Cosmologists John Barrow and Douglas Shaw of the University of Cambridge have now created a model1 that explains the time coincidence and naturally cancels out just enough of the quantum vacuum repulsion so that vacuum energy can account for the accelerating expansion of the Universe.

Making waves

Barrow and Shaw started by considering the entire Universe as a quantum mechanical wavefunction, which keeps the total energy of the Universe constant but varies other quantities such as its mass, age and shape, as well as the cosmological constant itself.

“There's no wiggle room with our model; it's either right or wrong.” Douglas Shaw

The University of Cambridge

The one important constraint was causality: anything that factors into these equations must also be consistent with what an observer on Earth can see. For instance, a contribution to the wavefunction from Alpha Centauri — a binary star system about four light years (1.34 parsecs) away from our Sun — would have to be consistent with the properties of the star as it was four or more years ago, inferred from current observations.

The researchers also weighted the different possibilities represented in the wavefunction according to how consistent they were with the predictions of general relativity and the standard model1,2. Like optical and acoustic waves, these alternate realities or different 'histories' interfere with one another, some cancelling each other out and others overlapping and reinforcing each other. In the surviving histories that weren't cancelled out, the authors found that the cosmological constant was fixed even though other properties of the Universe fluctuated. Then, they plugged in measurements for these properties and found that the predicted cosmological constant matched observations.

Rewriting history

Barrow and Shaw's calculations showed that in each surviving history, the constant is the same everywhere in the Universe throughout all of time — as had been assumed by physicists. But they found that the wavefunction's dominant histories can change.

"As time goes by, the longer photons have to arrive, and the more of the Universe we see," says Shaw. This alters the weighting of the different histories, bringing new combinations to the fore and resulting in a changing cosmological constant that is tied to the age of the Universe we inhabit.

"I certainly find the premise interesting but cannot agree with the logic," says astrophysicist Niayesh Afshordi of the Perimeter Institute in Waterloo, Ontario, Canada. He says that different observers at different times and places in the Universe seeing different values of the cosmological constant seems paradoxical when the rest of the Universe obeys classical laws. Shaw argues that because different observers are in different histories, their inability to communicate means that they each perceive a consistent, classical Universe.

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Although the shifts in the cosmological constant are not observable, Shaw and Barrow used the wavefunction that now dominates to predict the curvature of space by plugging in the measured cosmological constant. This number indicates that the Universe is sphere-like if the parameter is greater than one, a flat Universe if it is exactly one, and a saddle-shaped curvature if less than one.

In their upcoming paper in Physical Review Letters1, the authors place the value at 1.0056, predicting a very slight spherical curvature (see also ref. 2). This is consistent with observations from the Wilkinson Microwave Anisotropy Probe (WMAP) — a NASA mission launched in 2001 to measure the properties of the oldest light in the cosmos and use it to deduce fundamental properties of the Universe — which puts the curvature between 1.0133 and 0.9916.

But the European Space Agency's Planck satellite, launched in 2009, could prove or disprove Barrow and Shaw's idea within two years. Planck is WMAP's successor, and will be able to give an even more precise value for the curvature of the Universe.

"There's no wiggle room with our model; it's either right or wrong," says Shaw. And if they're right, it looks like cosmological history can indeed be rewritten.