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February 7, 2023

Out of the Darkness
As dark matter, dark energy, and general relativity slug it out against rival theories, Glenn Starkman hopes to pick out the winner.
by Bob Swarup
FQXi Awardees: Glenn Starkman
March 15, 2011
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Case Western Reserve University
Glenn Starkman is stepping into an intellectual boxing ring and taking on a daunting role—that of the referee. In one corner stands the ultimate physics heavyweight, Albert Einstein, whose theory of general relativity is hailed as one of the great triumphs of the 20th century. But in recent decades, general relativity has failed to explain a number of cosmic observations, leading some to argue that it’s fraying round the edges and to propose their own alternatives. Starkman is looking for ways to decide which of these rivals will emerge from the arena triumphant.

“The question is: Are we able to test these alternatives to general relativity?” says Starkman, a physicist at Case Western Reserve University in Cleveland, Ohio.

You could say that this is the $64,000 question. Or rather the $64,760 question, since that is the size of the grant that Starkman has been awarded by the Foundational Questions Institute to investigate the problem.

Starkman didn’t always see himself as a physicist. Born in Toronto, Canada, his initial passion was neuroscience, but that gave way to a lasting fascination with how the universe worked, thanks to a mathematics professor at a local university. “I studied with Professor Moshe Shimrat just about every week from 7th grade until he died near the end of my high school career,” remembers Starkman. “He showed me the beauty of the abstract, while encouraging my interest in the measurable.”

A PhD at Stanford University with Savas Dimopoulos focused his curiosity further on the universe. And the “interest in the measurable” that Professor Shimrat instilled in him all those years ago never dimmed, leading Starkman to today investigate how to test general relativity and its rivals.

He showed me the
beauty of the abstract,
while encouraging my
interest in the
- Glenn Starkman on Moshe Shimrat
General relativity has been extremely successful; so it’s no wonder that physicists hold it in high regard. However, standing alone, it cannot explain a host of strange observations. But rather than dare to modify the theory, physicists have invented a string of unexplained entities to explain the discrepancies. “So far, we have been forced to add three new forms only detected by their gravitational effects: dark matter, dark energy and the field that drives inflation,” says Starkman. “Many consider this contrived.”

Traditionally, the strongest evidence given for dark matter is that galaxies are rotating much faster than expected. Assuming that they are glued together by the gravity of the visible matter they contain, astronomers calculated that these galaxies are spinning so quickly they should have been torn apart long ago because there simply isn’t enough matter to hold them together.

The best solution to the puzzle seemed to be that the galaxies also contain vast amounts of unseen mass or dark matter, which provides the extra gravitational tug to keep everything in place. Astronomers were thus able to hold on to their theory of gravity, but at a cost: They had to accept that the majority of matter in the universe is in some unknown, invisible, form.

Which theory best explains
what happens when galaxies collide?

Credit: NASA
Dark energy is another mysterious entity, this time hypothesized to explain the acceleration of the universe’s expansion. Observed in the late 1990s, this acceleration again flew in the face of general relativity, which tells us that matter (including dark matter) should cause cosmic expansion to slow over time, thanks to its gravity. The solution? Add a new form of energy that pushes the universe apart more than the matter pulls it together.

The third worry for Starkman revolves around another burst of cosmic expansion, known as inflation, when the early universe went through an exponential growth spurt. Cosmologists need inflation to explain why the universe looks pretty much the same in every direction. Trouble is, general relativity can’t explain why inflation happened based on the currently observed contents of the universe; so physicists are left positing the existence of some enigmatic field—an early form of dark energy—that caused a similar accelerated expansion in the early universe.

Pretenders to the Throne

But there are alternatives to bolting on new entities like dark matter, dark energy, and the field driving inflation. “There has been longstanding interest in modifying general relativity as an alternative to repeatedly adding new forms of energy to the universe,” says Starkman.

The idea of modifying gravity was introduced in the mid-1980s. Mordehai Milgrom proposed a theory known as MOND (Modified Newtonian Dynamics), which tweaked the laws of gravity in different ranges in order to explain the weird galaxy-rotation observations.

We’ve been forced to add
dark matter, dark
energy and the field
that drives inflation.
Many consider that
- Glenn Starkman
Tinkering with gravity isn’t trivial. Any pretender must be able to explain the effects predicted by general relativity, such as how light bends around matter, and it must also explain the formation and layout of galaxies and clusters and the subtle patterns seen in the cosmic microwave background—the relic radiation left behind by the big bang.

Unfortunately, while MOND sounded great in principle, the idea hadn’t been developed well enough to be tested or to make predictions in the way that general relativity had. “Until then, you couldn’t really do cosmology or hope to understand how (complicated) systems behaved,” explains Starkman.

The dam began to break in 2004 with the arrival of Tensor-Vector-Scalar (TeVeS) theory, developed by Jacob Bekenstein at the Hebrew University of Jerusalem, Israel. TeVeS not only reproduced MOND’s predictions but also satisfied the principles of relativity.

Since then, others have built on Bekenstein’s success; Starkman and his collaborators recently introduced Generalized Einstein Aether, a class of theories that both generalize and simplify TeVeS.

Testing Times

OK, so now cosmologists have a bunch of theories that can take on general relativity. But how do you choose between them? One particular model of modified gravity, DGP—named after its proposers Dvali, Gabadadze and Porati—set Starkman thinking about how to test all these new varieties.

Supernovae told us the
expansion of the universe
is accelerating. But why?

Credit: Chandra X-Ray Observatory
Investigating DGP with two colleagues, Arthur Lue and Roman Scoccimaro, Starkman showed that when you alter gravity on cosmological scales, it has a knock-on effect on other things which, crucially, can be measured. For instance, you could potentially see the effects on the growth of cosmological structure and in the way that light bends around matter.

But intriguingly, their calculations also showed these effects were not specific to DGP. Rather, they were general features of a class of theories that obey something known as Birkhoff’s theorem.

Birkhoff’s theorem is a little known but vital conjecture that, loosely phrased, says the gravity inside a region is independent of the matter outside it. It greatly simplifies calculations in general relativity; without it, to work out the acceleration of a body at one place you’d need to know the position of all the matter in the universe—a complex undertaking, indeed.

None of the well-developed alternatives to general relativity proposed to date obey Birkhoff’s Theorem. So, asks Starkman, can we actually compute reliably with them? And if not, then what do we do?

Starkman is using his $64,760 FQXi grant to find out the answers. If reliable calculations can be done, then physicists can test these modified gravity models against future observations. But if not, things get awkward.

Glenn Starkman is always
willing to explore
questions that may be
outside the mainstream.
- Lawrence Krauss
“This won’t mean the models are wrong, just that they can’t be tested,” says Starkman. “In many ways, this is worse because it places them beyond the boundary of what most understand to be science.”

Although Starkman is only at the start of this journey, he is looking forward to digging deeper. Intriguingly, there’s an exception that doesn’t flout Birkhoff. Despite its other flaws, MOND—the granddaddy of modified gravity theories—maintains Birkhoff’s theorem and Starkman is keen to understand what this implies.

In the meantime, Starkman’s peers have high hopes for this latest research strand.

“Glenn Starkman is a creative physicist who is always willing to explore questions that may be outside of the mainstream,” says Lawrence Krauss at Arizona State University, Tempe. “The question is interesting and may be relevant to understanding dark energy.”

Tom Zlosnik at the Perimeter Institute in Waterloo, Ontario, agrees. “The research questions the validity of a deep assumption in cosmology,” he says. “The next genuine advance in physics may involve a dramatic development in our conception of the universe. Perhaps this stuff might be a step towards that.”

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