Relativity is the reigning theory of gravity. In situations where we can measure it directly, such as binary neutron stars, its predictions match the real world with remarkable precision. And, when supplemented with inflation and dark matter, relativity nicely reproduces the large-scale structure of the Universe. But this reliance on other models like dark matter means that we don't have a direct, large-scale test of relativity. Now, scientists have measured the redshifting of light by galaxy clusters to give use the biggest test of relativity yet. Their results show that relativity passes muster, while modified forms of Newtownian gravity fall short.

Light emitted by distant objects rarely makes it to Earth at the same wavelength that it started out at. The fabric of the Universe is expanding, which causes a redshift. Most objects are also moving relative to the Earth, which adds a Doppler shift to the light. Finally, light that has to climb out of a large gravity well on its way to Earth also gets red-shifted.

In theory, it should be easy to account for the distance and Doppler shift; anything that's left over should be the effect of gravity. Unfortunately, even with something as massive as a galaxy cluster, the gravity-induced redshift is about two orders of magnitude smaller than a typical Doppler shift. On top of that, the motion of galaxies within clusters should be random relative to the Earth, creating a broad, Gaussian distribution of color shifts. Picking a gravitational signal out of that curve would require a large data set to help cut down on the statistical noise.

Thanks to the Sloan Digital Sky Survey, we now have an absolutely enormous data set, containing over 7,800 galaxy clusters. The authors identified the brightest galaxy in a cluster, defined that as the cluster's center, and used it to calibrate the red shift of the cluster due to distance. From there, they calculated the relative red and blue shifts of all nearby galaxies.

This created the expected Gaussian curve. The flat sections of the curve represent galaxies that were in the field of view, but not gravitationally associated with the cluster. Within the cluster, the random relative motion of the galaxies relative to Earth creates a rounded peak. The authors were able to look for deviations from the expected Gaussian curve, and relate those to the predicted mass of the cluster in order to test for a gravitational red shift.

It worked. With a 99 percent confidence level, they've detected a gravitational red shift effect that is consistent with the one predicted by relativity, provided the mass takes into account the predicted levels of dark matter.

The relativity/dark matter combination, however, is just the most successful theory of gravity; it's not the only one. Some researchers have been attempting to develop a form of modified Newtonian dynamics (MOND) that is consistent with relativity, called the tensor-vector-scalar (TeVeS) theory. So, the authors plugged TeVeS into their calculations instead, and checked whether it could account for the effects they had detected. Close to the center of the cluster, TeVeS worked just as well as relativity. But at larger distances, the predictions and measurements start to diverge, and the authors conclude they can reject TeVeS with a 95 percent confidence.

The authors note that this measurement isn't dependent on any specific assumption about the structure of the Universe; it simply measures the ability of TeVeS to predict the behavior within galaxy clusters. "This implies that the discrepancy between TeVeS theory and the observations is unlikely to be a consequence of a specific choice of cosmological parameters," they write, "but indeed points to the inadequacy of this model to describe the Universe on very large scales."

So dark matter is in, MOND is out. What about inflation and dark energy? The authors plugged a dark energy model called f(R) into their calculations. Even under some unfavorable assumptions, dark energy remained consistent with the data from the galaxy clusters, so that it was impossible to distinguish between relativity and dark energy and relativity alone. If we wait a few billion years, it should be possible to get a clearer answer (my conclusion, not that of the authors).

The authors wrap up the paper by citing past results on gravitational red shifts, showing that they've now been detected everywhere from lab experiments on Earth to large galaxy clusters: "These results make gravitational red-shift the only effect predicted by general relativity that has been confirmed on spatial scales spanning 22 orders of magnitude." Overall, an impressive feat.

Nature, 2011. DOI: 10.1038/nature10445 (About DOIs).