The Patchwork Multiverse

Cutting spacetime into patches could help explain the size of the universe—and provide the first ”experimental” evidence that string theory is on the right track.

FQXi Awardees: Raphael Bousso

February 9, 2012

One man’s abstract is another man’s concrete. Nearly all ordinary folk, and even some physicists, would consider string theory to be a highly theoretical enterprise. But to Raphael Bousso, strings are intimately tied to understanding the universe we see around us. "The motivation is to understand how Nature works, and what’s going on out there," he says.Which is just as well, for Bousso is trying to solve one of the biggest puzzles in the cosmos: Just why is the universe so large? Bousso’s quest has led him to consider a multitude of universes and, in particular, how the value of the cosmological constant—the intrinsic energy of the vacuum of spacetime—could vary across different universe patches. The answer, Bousso claims, is "the first example of an experimental success of string theory."

It makes sense to look for a connection between the cosmological constant and the size of the universe. Many physicists believe that vacuum energy is the mysterious "dark energy" that is causing the expansion of the universe to accelerate. To fit with the cosmos that we see around us, the value of the constant should be small. The trouble is that this is in violent disagreement with calculations of vacuum energy from quantum field theory, by some 120 orders of magnitude.

In 1997, Steven Weinberg, of the University of Texas, Austin, came up with the first realistic prediction for the value of the cosmological constant. Weinberg noted that there comes a time in the evolution of the universe when the cosmological constant—which repulses gravity and causes spacetime to expand faster and faster—becomes dominant. He realized that if the constant was much larger than 10

^{-120}, it would dominate the universe too early, before galaxies, and in turn life, could be formed.

Underpinning the Universe

This allowed Weinberg to ask the question: What’s the most likely value of the cosmological constant that would be seen by observers in our universe? The answer: 10

^{-120}. Weinberg’s prediction was borne out by experiments to within a few orders of magnitude. "But the thing that was missing from the whole story was the theoretical underpinning," says Bousso.

As Weinberg himself noted, his arguments made sense only if there were many, many patches of spacetime, each with its own randomly-determined value of the cosmological constant. But in 1997, there wasn’t a theory that could generate different patches of spacetime, each with a different vacuum.

This is the first example of an experimental success of string theory.

- Raphael Bousso

^{500}vacua of spacetime. Essentially, each vacuum represents a different universe, each with different values for the cosmological constant and with different particles and forces.

The physical realization of this ensemble is referred to as the multiverse. With this theoretical underpinning in place, Bousso and Polchinski asked the same question that Weinberg did: What would be the most likely value of the cosmological constant that would be seen by an observer? They were able to show that the landscape would have regions with a cosmological constant that tallied well with observations.

But soon it became clear that the analysis suffered from a profound problem: How do you calculate the number of observers in a seemingly infinite universe?

Bousso’s answer was to limit himself to thinking only about an imaginary observer who lives forever. Because of the finite speed of light, this observer can only see events within a certain region of their universe—their

*causal patch*. Bousso has calculated that the size of the causal patch doesn’t change much over the lifetime of the long-lived observer. But inside this causal patch, the cosmological constant has a tremendous effect. As soon as it becomes dominant, it starts to accelerate the expansion of spacetime, and very soon dilutes the matter inside the causal patch.

"If the cosmological constant starts becoming important before the observers form, then there just won’t be very many observers opening their eyes in the region where you are allowed to count them," says Bousso.

Time of Life

Using the causal patch technique, Bousso found that the cosmological constant is related to the time at which observers inhabit any given universe. Plugging the age of our universe into his equations gave Bousso a universe that would be about 10

^{61.5}Planck lengths across and would have a cosmological constant of 10

^{-123}—both of which agree with observations. In fact, the value of the cosmological constant obtained in this manner is more precise than the one calculated by Weinberg.

Is Evidence of Dark Energy Also Evidence of the Multiverse?

The distribution of galaxies in a universe without dark

energy (left) would differ from one in which

dark energy is significant (right).

Credit: Lawrence Berkeley National Laboratory

So, the origin of these numbers—why the cosmological constant is not smaller and why the universe is not bigger—has to do with the finiteness of the string landscape, explains Bousso.

"It actually explains the cosmological constant in a way that previous theoretical attempts have utterly failed," he says.

At the 2011 FQXi conference, Bousso discussed the relationship between time and the multiverse:

The challenge going forward is to get a better handle on the string landscape. For instance, in their latest paper, which was work done using an FQXi grant of over $60,000, Bousso and colleagues predict that the string landscape will have about 10

^{123}so-called meta-stable vacua that could give rise to habitable universes in which observers could form (arXiv:1011.0714v2).

This explains the cosmological constant in a way that previous attempts have utterly failed.

- Raphael Bousso

Bousso has been successful in taking nebulous questions and coming up with something concrete, says Polchinski. "His conclusion is something that can eventually be refined into a sharp mathematical prediction."

Sharp predictions are exactly what string theory needs, to counter criticisms that the theory is too far removed from reality. But Bousso has long been convinced that he is on the right track. "I think the evidence is mounting that there really is a multiverse and that there all these vacua there," he says. "I don’t think we can claim victory yet, but there is really no other game in town."