Galaxy Clusters Validate Einstein’s Theory – and Dark Matter Too

The theory of relativity – both special relativity and general relativity – has now been tested successfully so many ways ever since its early days that further tests seem almost redundant. (That little mix-up with superluminal neutrinos to the contrary notwithstanding – since it’s at most a higher order correction, but more likely an error in data interpretation.) But science never stops testing if there’s some creative new way to do so. And that’s what’s involved here.

One of the predictions of general relativity is that light photons lose energy when climbing out of a strong gravitational field. In that case, the light should be redshifted, in a way that doesn’t involve either a Doppler effect or the expansion of the universe.

It takes a very strong gravitational field to make this gravitational redshift apparent. Even a single galaxy isn’t large enough. But a cluster of galaxies will do, although the effect is almost masked by relative motion of galaxies in the cluster. However, in a cluster there’s a fairly straightforward way to check, since the shift should be larger with photons from the center of the cluster than from the periphery, as the gravitational field is stronger at the center.

Galaxy Clusters Validate Einstein’s Theory – ScienceNOW

Wojtak and his colleagues knew that measuring gravitational redshifting within a single galaxy cluster would be difficult because the effect is very small and needs to be teased apart from the redshifting caused by the orbital velocity of individual galaxies within the cluster and the redshifting caused by the expansion of the universe. The researchers approached the problem by averaging data collected from 8000 galaxy clusters by the Sloan Digital Sky Survey. The hope was to detect gravitational redshift “by studying the properties of the redshift distribution of galaxies in clusters rather than by looking at redshifts of individual galaxies separately,” Wojtak explains.

Sure enough, the researchers found that the light from the clusters was redshifted in proportion to the distance from the center of the cluster, as predicted by general relativity. “We could measure small differences in the redshift of the galaxies and see that the light from galaxies in the middle of a cluster had to ‘crawl’ out through the gravitational field, while it was easier for the light from the outlying galaxies to emerge,” Wojtak says.

In addition to further confirming relativity, this research may also rule out some alternative theories of gravity that have been proposed to avoid the hypotheses of dark matter and dark energy, which are needed with standard relativity to explain many astronomical observations – and do so very well.

One of the alternative gravitational theories, Modified Newtonian Dynamics (MOND) attempts to avoid the need for dark matter by adding fudge factors to Newton’s equations of motion. There is also an extension of MOND, “tensor-vector-scalar” (TeVeS) theory, which stands in relation to MOND as general relativity is to Newton’s equations. Both of these theories seem to be incompatible with the gravitational redshift results. Another alternative theory, f(R) gravity, which attempts to avoid the need for dark energy, may still be viable.

Galaxy clusters back general relativity

The Copenhagen group discovered that the redshifts agreed with the predictions of both general relativity and f(R) gravity, the theory that tries to avoid dark energy. However, the error bars on the redshifts excluded MOND and TeVeS, the theories that try to avoid dark matter. This backs the conclusions of a separate galaxy study performed earlier this year – but the Copenhagen study has the added clout that it has not been based on any assumptions of the generally accepted ΛCDM model.

“I always find it remarkable how general relativity performs well in all the tests we can conceive,” says Alberto Cappi, an astronomer at the Observatory of Bologna, Italy, who tried to perform a similar study in 1995. “Of course the error bars are large, and it is difficult to see a statistically significant trend…but it is true that the relativistic version of MOND [TeVeS] does not perform well in describing the data.”

An important aspect of the current study is that it does not depend on knowing the distances of the many clusters observed in the study, so that no assumptions about the existence and nature of dark matter and dark energy need to be made. Instead, the key factor in the study is the pattern of variability of gravitational redshift from the centers to the edges of clusters. A dependence on assumptions about dark matter and dark energy is why direct tests of general relativity on a cosmic scale haven’t been possible before. The way in which gravitational redshift varies in the clusters is what favors the dark matter hypothesis over MOND and TeVeS, because the pattern requires mass in addition to that supplied by ordinary matter.

Galaxy clusters back Einstein, leave Newton’s descendants in the cold

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.”

Wojtak, R., Hansen, S., & Hjorth, J. (2011). Gravitational redshift of galaxies in clusters as predicted by general relativity Nature, 477 (7366), 567-569 DOI: 10.1038/nature10445

Further reading:

Light from galaxy clusters confirm theory of relativity

Galaxy Clusters Validate Einstein’s Theory

A New Test of Dark Matter vs. Modified Gravity: Who Wins?

Gravitational redshift of galaxies in clusters as predicted by general relativity

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