Einstein's General Theory of Relativity explains gravity in terms of the curvature of space by mass. Dating from the second decade of the 20th century, after more than 90 years it is still the basis of our understanding of how gravity works to shape the cosmos.

But as evidence for a universe filled with dark matter and dark energy has mounted, General Relativity's ability to explain the structure and expansion of the universe has faced new challenges.

Some theorists deny that dark matter or dark energy exist, suggesting that there's a problem with General Relativity's handling of gravity. They hope to explain away the apparent gravitational effects of dark matter, and the apparent accelerating expansion of the universe caused by dark energy, with appeals to modified gravitational theories.

"One of the first proper theories of modified gravity is called the tensor-vector-scalar theory, or TeVeS," says Uros Seljak, a member of Berkeley Lab's Physics Division, who is also a professor of physics and astronomy at UC Berkeley and a professor of physics at the University of Zurich. "By a 'proper' theory, I mean one that makes definite predictions about what we should be able to observe if it is true."

Testing predictions about the shape and growth of the cosmos requires measurements on the scale of the cosmos itself. Only in recent years have surveys like the Sloan Digital Sky Survey (SDSS), which has collected spectra of well over a million distant stars, quasars, and galaxies since it began operation in 1998, made such universe-spanning measurements possible.

Now Seljak and a group of colleagues including some of his current and former students, as well as James E. Gunn, founder of SDSS, have analyzed some 70,000 red luminous galaxies from SDSS's collection to test the TeVeS theory of modified gravity, and with it another modified theory of gravity called f(R), which seeks to explain the accelerating universe without recourse to dark energy.

"Our measurement combines gravitational lensing, galaxy clustering, and the growth rate of the large-scale structure of the universe," Seljak explains. "No one of these by itself could test modified gravity theories because of large uncertainties in the observations at cosmological distances."

The collaborators report their findings in the March 11, 2010 issue of Nature. First authors of the paper are Princeton University graduate student Reinabelle Reyes and recent Princeton Ph.D. Rachel Mandelbaum. With Seljak and Gunn, the other authors are Tobias Baldauf, Lucas Lombriser, and Robert E. Smith of the University of Zurich.

Combining measurements to reduce uncertainty
An important source of uncertainty in cosmological measurements is so-called "galaxy bias," which can be observed as the change in the way galaxies cluster according to what type of galaxies they are, for example blue galaxies or more luminous red ones.

One explanation is that galaxy bias is due to the difference between the distribution of galaxies and the distribution of the invisible dark matter that underlies them - but this doesn't help when testing a theory that says there's no such thing as dark matter.

"Galaxy bias is one of those 'nuisance parameters' that tells us nothing by itself," says Seljak. "Because it tells us nothing on its own about dark matter or dark energy or other cosmological ideas, we'd like to get it out of the way."

Galaxy bias can essentially be bypassed by combining measures of gravitational lensing - the way intervening mass bends the light from more distant luminous objects, making them appear distorted - with galaxy clustering and the growth of structure. The three together yield a quantity called EG, originally proposed by Pengjie Zhang of Shanghai Observatory and his collaborators as a way to test cosmological models.

Modified gravitational theories don't predict the same value of EG as General Relativity (with dark matter thrown in) when it comes to comparing the mass density of the universe to the growth of its structure. In general, modified theories predict faster growth of structure, making EG smaller.

Growth rate can be calculated from redshift surveys, which measure velocities of galaxies. Galaxy clustering and weak gravitational lensing - which must be used at cosmological distances, where the distorted shapes of background galaxies can't be measured directly but have to be derived statistically - can be used to estimate mass density.

The value of EG that Seljak's colleagues obtained from their deeper-than-ever probe of cosmological growth still has a large uncertainty, some 16 percent. Even with wide error bars, however, the value is enough to exclude the predictions of the TeVeS "no dark matter" theory.

The best fit of the value of EG from this survey assumes that dark matter exists and General Relativity is correct. The uncertainty is still too great to rule out f(R) theories that modify gravity so as to exclude dark energy, however.

"To test theories that do away with dark energy, we'll need much larger data sets for better control of systematic errors," says Seljak. "Fortunately, SDSS-III is now underway, with most of its telescope time devoted to BOSS."

BOSS, the Baryon Oscillation Spectroscopic Survey led by David Schlegel of Berkeley Lab's Physics Division, will collect data from over a million and a half luminous red galaxies and quasars.

Though BOSS's main purpose is to provide an independent measure of dark energy through the technique called baryon acoustic oscillation, the data from BOSS will be some of the best ever obtained on the large-scale structure of the universe and can be used to narrow the uncertainty of measuring EG.

As to whether or not Einstein needs to be updated, the final answer may have to await BigBOSS, the joint Berkeley Lab/National Science Foundation proposal to survey some 50 million galaxies in both the northern and southern hemispheres over a 10-year period. BigBOSS would produce an astonishingly wide and deep survey of the sky, enough to tighten the error bars around the best gravitational theory of all.

Will it be General Relativity after all? Stay tuned.