*Does correcting an error in the way cosmologists applied Einstein’s equations solve the mystery we call Dark Energy?*

About a year ago, I completed a fascinating online lecture series from a company called *The Great Courses* called *What Einstein Got Wrong*. People tend to think that Einstein was superhuman, correctly discovering everything about everything.

The truth is, he was human like the rest of us, and made mistakes. We can now say that his Theory of Relativity was astonishingly right. He was also right that light acts like both a wave and a particle, and about the photoelectric effect, for which he won the Nobel Prize.

On the other hand, he was wrong about a handful of important things as well. He was wrong to be skeptical about the probabilistic way that elementary particles behave. He famously said, “God does not play dice with the universe”. We now know that quantum mechanics is quite a bit like a crapshoot. He was also wrong to doubt that black holes exist, since his own equations accurately predicted them.

#### Einstein was wrong about his “cosmological constant”

Probably the most ironic thing that Einstein was wrong about was his “cosmological constant”. That’s a mathematical term he included in his equations to accommodate his belief that the universe could neither expand nor contract. When Edwin Hubble discovered that the universe is, in fact, expanding, he called his cosmological constant the “biggest blunder” of his career.

What makes this ironic is that, since 1996, scientists have had to reintroduce the cosmological constant. We now know that, not only is the universe expanding, its expansion is accelerating. For that to happen, something must be adding energy to the expansion’s momentum. Physicists can’t explain what that “something” is, so they call it “Dark Energy”.

They account for Dark Energy by re-inserting Einstein’s supposed blunder back into his equations. It turns out that Einstein’s real mistake was in thinking he had made a mistake in the first place. I’m not bringing these points up to make fun of Einstein. He’s still my hero, even after taking that course.

#### a fresh error in applying Einstein’s equations

I raise these concepts because they are in the news again this week. Researchers at the University of Hawaii at Manoa (there’s a cool job!) have found a fresh error in the way cosmologists have applied Einstein’s equations to the expansion of the universe. This isn’t so much Einstein’s mistake as it is that of those who came later.

We’ve always thought that the overall universe is
far too vast to be affected by individual objects inside it. Kevin
Croker, a postdoctoral research fellow in the Department of Physics and
Astronomy, and Joel Weiner, a faculty member in the Department of Mathematics
have now shown us that when supermassive stars collapse, they become so dense
that they do, in fact, affect the universe itself. Their discovery appears in *The Astrophysical
Journal*.

As Dr. Croker puts it, “For 80 years, we’ve generally operated under the assumption that the universe, in broad strokes, was not affected by the particular details of any small region. It is now clear that general relativity can observably connect collapsed stars — regions the size of Honolulu — to the behavior of the universe as a whole, over a thousand billion billion times larger.”

#### we need to take unimaginably dense objects into account.

Traditionally, cosmology has assumed that, on average, the universe is more or less uniform in its density. This new research suggests that we need to take the unimaginably dense objects left over after stars collapse into account. Their average distribution throughout space influences the behaviour of the universe overall.

When I mentioned massive stars collapsing, readers’ minds probably jumped to black holes. It’s true, many of the more massive stars do turn into black holes when they die, but maybe not all of them. In 1966, Erast Gliner, a Russian physicist, proposed something we now call Generic Objects of Dark Energy (GEODEs). He suggested that they would also be a remnant of collapsed stars. Cosmologists distinguish them from black holes because of what they contain.

Readers will recall that the inside of a black hole is so dense that the laws of physics break down. We call this a singularity. The inside of a GEODE is different. Gliner believed that the inside of a GEODE contained the mysterious Dark Energy discussed above. When Croker and Weiner corrected the math we talked about, they realized something remarkable. If these proposed GEODEs exist, their Dark Energy might be what boosts the expansion of the universe.

#### Mergers create gravitation waves

In an earlier story, we talked about collisions between dense objects like black holes and neutron stars. We saw how these mergers create gravitation waves (something else that Einstein was right about!) that are picked up by sophisticated new instruments like LIGO and Virgo. Something we didn’t cover is that the objects in these collisions seemed to be more massive than expected. When Croker and Weiner applied their new math, they found that, if these objects were GEODEs instead of black holes, it would explain this puzzling discrepancy.

We can all learn from this weeks’ discovery. What it teaches us, above all, is that mistakes are how we learn. When Croker and Weiner corrected those obscure errors in the application of Einstein’s equations, they may have started a revolution. Dark Energy is the biggest mystery in modern cosmology. Since it makes up about 2/3 of our universe, that’s frustrating for science. Assuming there really is such a thing as a GEODE, their new math might be the solution scientists need.

Having said that, their hypothesis rests on a pretty big assumption. Nobody has ever seen or detected a GEODE in the real world. They would be the first to admit that. As they say, “What we have shown is that if GEODEs do exist, then they can easily give rise to observed phenomena that presently lack convincing explanations. We anticipate numerous other observational consequences of a GEODE scenario, including many ways to exclude it. We’ve barely begun to scratch the surface.”

We always have more to learn if we dare to know.

Learn more:

University of Hawaii

Implications of Symmetry and Pressure in Friedmann Cosmology

What Einstein Got Wrong*The 5 Big Questions We Need Cosmology to Answer**Cosmic Collision Makes Waves*