A neat way of measuring the geometry of the Universe offers a new test of the standard cosmological model. It probes, among other things, the elusive dark energy thought to be driving the Universe's expansion. **See Letter** p.539

Twenty years ago, most cosmologists thought the Universe was dominated by a large amount of dark matter, and the idea of dark energy was no more than a curiosity. Now, as a result of exquisite observations of the radiation left over from the Big Bang, the large-scale structure of galaxies and distant supernovae, all that has changed: we have a generally accepted 'standard cosmological model', in which 23% of the energy density of the Universe is in the form of dark matter, 73% in dark energy, and only 4% in the form of the ordinary matter that we know on Earth. On page 539 of this issue, Marinoni and Buzzi^{1} describe a new technique for testing the cosmological model that is completely independent of previous methods.

To say the finding that dark energy contributes about three-quarters of the total energy density of the Universe was unexpected would be an understatement. Gravity slows the expansion of the Universe, and yet the Universe isn't playing ball — its expansion rate is actually accelerating, and this requires a component of the Universe with a repulsive gravity, a role thought to be played by dark energy. Not surprisingly, many cosmologists regard determining the nature of dark energy and dark matter as the most important scientific question of the decade.

Our picture of the Universe involves putting together a number of pieces of evidence, so it is appealing to hear of Marinoni and Buzzi's novel technique^{1} for testing the cosmological model, not least because it provides a very direct and simple measurement of the geometry of the Universe. One of Einstein's most remarkable insights was that the geometry of the Universe depends on its contents. So we can use geometrical measurements to determine the amounts of dark matter and dark energy, and the nature of the latter.

The general idea of Marinoni and Buzzi's technique goes back to Alcock and Paczyński^{2} and, curiously, exploits the fact that we cannot directly measure distances in cosmology — there is no prospect of placing rulers between us and a distant galaxy. Instead, we rely on Hubble's law, which states that the speed of recession of galaxies is proportional to distance. The speed can be measured using the Doppler effect, which shifts the galaxy light to the red end of the electromagnetic spectrum, hence the use of the term redshift in astronomy to describe how far away a galaxy is. For large distances, the argument is modified, but higher redshift still indicates greater distance. The bottom line is that the way that redshifts and angles on the sky (both of which are directly observable) translate to positions (which are not) depends on the geometry of the Universe.

So imagine we have a distant object that is completely spherical and expanding along with the rest of the Universe. By measuring the redshifts of different points on the surface of the sphere, one can map out the shape of the object, using the formula for changing redshifts and angles to positions. If we assume the correct contents and geometry of the Universe in the formula, the object will indeed appear to be spherical, but if we do not, the sphere will appear to be distorted. This is the essence of Alcock and Paczyński's idea. The key, of course, is to find spherical expanding objects, which unfortunately do not exist. However, one can be more subtle, and use something less tangible.

Marinoni and Buzzi^{1} use the distribution of orientations of galaxy pairs in orbit around each other in binary systems. We expect the orientations to be completely random, with all orientations being equally likely — that is, the distribution of pairs is spherically symmetric. Only if we choose the correct contents and geometry (that is, the cosmological model that truly represents the Universe) in the calculation of the pairs' orientation, will the orientations appear to be evenly distributed (Fig. 1). So the authors^{1} vary parameters that quantify the contents and the geometry until they find the values that best fit a random distribution.

This exercise needs to be done for very distant galaxies, several billion light years away, because the effects of different geometries are only substantial on very large scales. The main complication is that a galaxy's redshift, which enters the calculation of the orientations, has two components: a cosmological component arising from the expansion of the Universe and an additional Doppler component from the speed of the galaxy in orbit. This additional component distorts the distribution of angles, but in a known way that depends on the distribution of orbital speeds. Marinoni and Buzzi measure this distribution from nearby galaxies, and use it to analyse pairs of galaxies at high redshift in the DEEP2 galaxy redshift survey^{3}.

The authors^{1} find consistency with the standard cosmological model, with its flat geometry, and show that the dark energy is consistent with being a vacuum energy, which can be represented by Einstein's famous cosmological constant. How might their technique fail? Clearly, we have to be certain that different pair orientations are detected with equal probability and that the orbital speeds are independent of orientation, as the authors' method assumes. The distribution of orbital velocities of the pairs also needs to be known, and this is perhaps the point one might worry about most. This distribution can be investigated in the local Universe, but the distribution is then assumed to be the same at high redshift. Because of the finite light travel time, the distant galaxies of the DEEP2 survey are being seen as they were when the Universe was about half its present age, and galaxy-pair properties could have changed over that period. Nevertheless, Marinoni and Buzzi's study offers a novel and imaginative idea.

## References

- 1
Marinoni, C. & Buzzi, A.

*Nature***468**, 539–541 (2010). - 2
Alcock, C. & Paczyński, B.

*Nature***281**, 358–359 (1979). - 3
Davis, M. et al.

*Astrophys. J.***660**, L1–L4 (2007).

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Heavens, A. Geometry of the Universe.
*Nature* **468, **511–512 (2010) doi:10.1038/468511a

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