What does space look like at a really, really small scale? Answering that question could resolve one of the most difficult problems in modern physics, the huge mismatch between Einstein’s General Relativity, quantum theory and the measured acceleration of the expansion of the universe

Cosmologists have known for about 20 years that the universe is not just expanding, but that the expansion is speeding up. To explain this cosmic acceleration, theoretical physicists invoked “dark energy,” a force that emerges from quantum fluctuations of the vacuum of space and pushes the galaxies apart.

Einstein’s theory of general relativity includes a value for the vacuum energy of space, the cosmological constant. When Einstein proposed general relativity in 1915, the universe was thought to be static. So he included the cosmological constant in his equations to counter gravity and prevent the universe from collapsing on itself. In the 1930s, astronomers found that the universe was expanding from the Big Bang and Einstein abandoned the idea as a mistake.

The discovery of cosmic acceleration and dark energy caused theorists to take another look at the cosmological constant. But there is a problem.

“We don’t really know how to calculate the cosmological constant,” said Steve Carlip, distinguished professor of physics at UC Davis. “Methods that work in other contexts give an answer 60 to 120 orders of magnitude larger than the observed dark energy, which is pretty bad.”

## Foamy spacetime at a very small scale

Physicists have been tinkering with ways to cover this gap, including making tweaks to general relativity or invoking multiple universes with different cosmological constants. In a new paper published in *Physical Review Letters*, Carlip proposes a new direction that sees spacetime at a very small scale as a complex foamy structure.

The idea of spacetime foam dates back to the 1950s and cosmologist John Wheeler at Princeton University. Wheeler proposed that at the Planck scale – distances of 10 to the negative 35 meters, 100 million trillion times smaller than a proton – space would not be continuous, but foamy.

If you look at the ocean from a great height, Carlip said, it looks smooth. Get closer and you can see swells and waves. Closer still and you can see the foam and spray among those waves.

In the same way, the small-scale structure of spacetime would become apparent as you get close to it. Wheeler did not have the mathematical tools to build a model of foamy spacetime but these now exist.

Carlip’s new approach is to accept that the value of the cosmological constant really is huge as calculated, but that it does not necessarily have the same effect everywhere in the universe. In a model of spacetime made of tiny bubbles, the cosmological constant could cause opposite effects, acceleration or deceleration, in neighboring bubbles. These would tend to cancel each other out leaving only the small, residual effect that we see as dark energy.

“If you look at space at a fixed time and choose a complex structure, the cosmological constant is almost invisible,” Carlip said.

The new theory is a “direction to explore” not a complete solution, Carlip said. While it works at a point in time, it’s not clear how it would evolve other time. It’s also not clear how scientists could test the idea experimentally. But it could spur some new developments.

“The hope is this may give us some hints of where to go in the theory of quantum gravity,” Carlip said.