The faint microwave glow left over from the big bang has been measured with unprecedented precision, giving astronomers a new insight into the nature of the universe

The geometry of the universe is Euclidean and space is flat. This has now been confirmed from detailed measurements of the cosmic microwave background – the radiation left over from the big bang – by an international team of astronomers from Italy, the UK, the US, Canada and France. The Boomerang collaboration, led jointly by Paolo de Bernardis of the University of Rome and Andrew Lange of the California Institute of Technology, has measured the angular distribution of temperature fluctuations in the microwave background with unprecedented accuracy. Such fluctuations contain information about the energy density and curvature of the universe (P de Bernardis *et al* 2000 *Nature* **404** 955).

Einstein’s general theory of relativity predicts that gravity is, in effect, a curvature of space. This means that we can replace the gravitational field of the Sun by a slight curvature in the surrounding Euclidean space. The effect of this is that straight lines, as traced by light rays from distant stars, are no longer straight.

The deviation, which is tiny, was first observed in 1919 during a solar eclipse. The measurements showed that light from a distant star near the edge of the Sun was deflected by just 2 seconds of arc. This observation revolutionized modern physics.

Overnight, a new theory of one of the fundamental forces of nature was accepted. We had to abandon our precepts about the geometry of the universe being Euclidean.

Parallel lines were no longer parallel. Moreover, gravity could now explain one of the most challenging problems in physics – the origin of the universe.

The big-bang theory was a consequence of the theory of gravitation. The universe expanded in a precarious competition between the kinetic energy of the expansion and the gravitational potential energy that threatens to eventually cause the universe to contract. If there is enough matter in the universe, then gravity will dominate, the universe will decelerate and it will begin to contract. However, if the density of matter is below a critical value, called W_{critical} by cosmologists, then the universe will expand forever.

The critical density is well known and is given by 3*H*_{0}^{2}/8p*G*, where *G* is the gravitational constant and H_{0} is the Hubble constant, which has recently been measured to an accuracy of 10%. But what is not known is the actual density of the matter, most of which is known to be non-luminous or “dark” and thus exceedingly difficult to detect.

### Geometry, matter density and dark energy

There are, in fact, three possibilities for the geometry of the universe. It could be flat (or Euclidean) and resemble a sheet in 2-D. Alternatively it could have a spherical geometry and look like the surface of a sphere, or it could be hyperbolic and resemble a saddle-shaped surface in 2-D. Each geometry offers an unbounded space that encompasses the entire universe.

General relativity predicts that if the universe is below the critical density, it will expand forever and have a hyperbolic geometry. Such a subcritical universe has a “positive” energy, which means that the kinetic energy associated with its expansion is much greater than its gravitational potential energy. In contrast, a universe in which the density of matter is greater than W_{critical} has a negative total energy. Meanwhile, a critical-density universe has zero energy. Einstein’s theory identifies the energy of the universe with the nature of its geometry. Only a critical-density universe is Euclidean.

Observations strongly hint that the matter density is subcritical. Although about 90% of this matter is dark, its gravitational effects allow us to measure its density. A variety of techniques point to a matter density that is one third of the critical value, with an uncertainty of a factor of two at the most. However, we cannot infer that the universe is destined to expand forever. There may also be “dark energy” present, which provides a repulsive force.

The concept of dark energy was originally introduced by Einstein in 1917, some 12 years before Edwin Hubble discovered that the universe is expanding. Einstein conceived the idea to counter the gravitational effect of matter and provide a static universe that neither collapsed nor expanded. He called this repulsive force the cosmological constant, which appeared as an additional constant in the equations of general relativity and had no Newtonian counterpart.

In 1930 Einstein became convinced of Hubble’s expansion law, and later admitted that the introduction of the cosmological constant was one of the greatest mistakes of his life. Meanwhile, others – notably Russian theorist Alexandre Friedmann in 1922 and Belgian cosmologist Georges Lemaitre in 1927 – predicted a universal expansion that culminated in Hubble’s discovery.

However, theory has a habit of rebounding and once Pandora’s box is opened, it becomes hard to close. Dark energy would never be forgotten, and the cosmological constant has regularly resurfaced to account for some particular observational challenge – and has invariably faded away again as observations improved.

The first real revival came from theory. In 1981 inflationary cosmology provided the first major new insight into the big bang since the 1920s. According to this model, the universe underwent a phase transition 10^{-35} s after the big bang and expanded exponentially in scale for a brief period. This period of rapid expansion flattened the geometry of the universe. Inflation predicts that the universe is at the critical density. Dark matter could not account for the critical energy, and the cosmological constant remained the plausible culprit, if inflation did indeed occur.

### Precision measurements

If we could directly measure the geometry of the universe, then we could bypass the dark-matter problem and test the inflationary prediction of flatness. Enter the Boomerang experiment. Designed to study the cosmic microwave background with unprecedented accuracy, this microwave telescope surveyed 2.5% of the sky with an angular resolution of 0.25^{o} during a 10-day balloon flight over Antarctica (figure 1).

One of the key pieces of evidence for the big bang is that the cosmic microwave background has a perfect black-body spectrum with a temperature around 2.73 K in all directions. However, theory predicts that there should be temperature fluctuations at the level of 10^{-5} in order to seed galaxy formation. Indeed, such fluctuations were discovered in 1992 by the COBE satellite, which had an angular resolution of 7^{o}.

The much higher resolution of the Boomerang experiment has enabled astronomers to make a fundamental test of the nature of the fluctuations. The primordial fluctuations are enhanced by the astrophysics of the early universe on small angular scales. These scales correspond to the maximum distance a fluctuation driven by pressure variations can propagate in the early universe. A peak in intensity occurs on the horizon of the universe 300 000 years after the big bang, when the matter and radiation ceased to interact via photon scattering. In the case of a flat universe, this peak is predicted to occur at a characteristic angular scale of 45 arcminutes.

This physical scale translates to an angular scale in the sky that depends on the curvature of the universe. If the universe is negatively curved, or has a lower density, the predicted peak shifts to smaller angles. In effect, the gravity field of the universe acts like a lens.

Boomerang has measured the peak with unprecedented precision and gives confirmation of the primordial origin of the fluctuations. Moreover, the measured peak agrees precisely with the expectation for a flat universe. The location of the peak means that the density of matter is within 10% of the critical value. The universe must therefore be dominated by dark energy – the modern reincarnation of the cosmological constant.

Tentative measurements of the distances to Type Ia supernovae show evidence that the expansion of the universe is accelerating, as predicted for a universe that is spatially flat but in which two-thirds of the critical density is accounted for by the dark energy associated with the cosmological constant (B P Schmidt et al. 1998 Astrophys. J. 507 46 and S Perlmutter et al. 1999 Astrophys. J. 517 565). Hence cosmologists are happy, and a consistent cosmological model beckons with independent verification of an unexpected key parameter from two totally independent experiments.

### Unexpected results

Life would be dull for cosmologists if all that emerged from Boomerang was confirmation of flatness and dark energy. Although the predicted peak at 45 arcminutes is at exactly the angular scale expected for the preferred flat model, the data continue to 15 arcminutes. Theory predicts a second feature due to the wave-like oscillations of the radiation pressure-driven fluctuations. This feature corresponds to the trough of the wave that peaked at 45 arcminutes and shows up in the power distribution as a second peak (figure 2). This second peak is smaller than the first because the radiation is “redshifted” very slightly during the time it takes the trough of the wave to become visible on the horizon of the universe.

The big surprise in the Boomerang data is that the amplitude of the second peak is smaller than predicted, although it appears to occur at the expected position. Within a week of the release of the first Boomerang results, the electronic Web servers buzzed with speculation about why this might be the case. Favourite among the preferred explanations is the idea that the density of ordinary or baryonic matter might be up to twice as large as indicated by the measured abundances of hydrogen, helium and lithium. Increasing the baryon density preferentially damps out the shorter-wavelength pressure waves, and reduces the amplitude of the second peak.

This is not a unique explanation, however, but it does lead to novel predictions. For example, the ratio of baryonic to non-baryonic dark matter is likely to be 25% or more. This suggests that a baryonic “footprint” may show up in galaxy surveys, such as the 2dF surveys on the Anglo-Australian telescope and the Sloan Digital Sky Surveys. Indeed, baryon-induced oscillations are expected to become visible in 3-D galaxy distributions stretching back 330 million light-years.

It seems to be inevitable in astronomy that each new discovery raises further challenges. The universe is flat, but absorbing the full implications of the Boomerang data will take some time, and will undoubtedly inspire new experimental efforts and new insights into the nature of the universe.