Stabilizing the no-boundary proposal sheds light on the universe's quantum origins

One idea for how the universe began is that the universe may have appeared out of nothing due to some quantum effect, such as quantum tunneling. In the 1980s, Stephen Hawking and James Hartle further elaborated on this idea by suggesting that time did not exist before the beginning of the universe, leading them to conclude that the universe has no initial boundary conditions on either time or space. The idea is called the "no-boundary proposal" or the "Hawking-Hartle state."

However, precisely describing how a physical system can transition from zero size to a finite size has been challenging. To describe the quantum effects involved, physicists use the path integral formulation, which involves rewriting a single classical trajectory as an integral over many possible trajectories, resulting in a quantum amplitude.

Although the path integral formulation is successful at describing how something can emerge from nothing, one major problem is that it predicts unstable perturbations, implying that the universe is highly non-homogenous and non-isotropic. As the universe is known to be approximately both homogenous and isotropic (meaning that it looks the same in all locations and from all directions), as stated by the cosmological principle, the path integral formulation doesn't accurately describe the observed universe. This has led some scientists to conclude that the no-boundary proposal cannot provide an accurate description of the universe's origins.

Now in a new paper, physicists Alice Di Tucci and Jean-Luc Lehners at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam, Germany, have shown that the path integral formulation can be used in a way that avoids instabilities, while still providing a consistent definition of the no-boundary proposal.

"I think that the biggest significance is that our new definition does not describe the emergence of the universe from a complete absence of space and time," Lehners told Phys.org. "Rather, the new mathematical conditions, that we had to impose to avoid instabilities, can be interpreted as saying that there existed already fluctuations of space and time. This is in fact what one might expect from quantum theory in any case, as the quantum uncertainty principle implies that there should always be fluctuations, presumably even of space and time."

The new proposal combines several ideas that have previously been suggested to overcome the problem with instabilities. Their work essentially changes the geometry of the space over which the path integral is defined. The path integral, which represents the state of the universe at a certain time, passes through certain critical points called saddle points, which correspond to possible Hawking-Hartle states.

However, most of these saddle points are unstable. One of the most important changes the physicists made in the new paper was to modify the boundary conditions on the entire geometry (by using Robin boundary conditions) to remove the unstable saddle points from the path of the path integral. In the new geometry, the path integral passes through only one saddle point, which is stable, therefore avoiding the problem with instabilities. At this stable saddle point, there exists a Hawking-Hartle state that satisfies the no-boundary proposal.

By demonstrating a stable method for formulating the no-boundary proposal, the results may lead to a rethinking of the idea as a description for the origins of the universe. Still, there are many questions that remain.

"In the future we plan to see how robust our new definition is when incorporating aspects from string theory, which is the most advanced attempt at a full theory of quantum gravity," Lehners said. "Also, we plan to explore whether other stable definitions of the no-boundary proposal might exist, or whether our new one is in some sense unique. And a big question that remains is whether we could deduce any testable/observable consequences."

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