**The Hartle and Hawking No-Boundary Proposal**

One of the problems of the inflationary theory is that it does not explain what may have occurred before the inflation of the universe. In an attempt to resolve this issue, James Hartle and Stephen Hawking proposed another theory in for the creation of the universe in 1983. The theory was based the idea that the universe did not have a boundary, just as the earth does not have a boundary. For example, one may travel around the earth and not come to a boundary or fall off. In addition, the theory was based on quantum theory, a superset theory encompassing general relativity and quantum mechanics.

Quantum theory defines a wave function that describes all of the possible states of a quantum particle, such as an electron. The values of the wave function indicate the probabilities of the particle being found in the various states. For example, if the value of the wave function is high for a particular state, then the particle is likely to be found in that state. Conversely, a low wave function value suggests that the particle is less likely found in that state.

Hartle and Hawking's new theory treated the universe like a quantum particle. As a result, they created a wave function that describe all possible universes. The wave function is assumed to have a large value for our own universe, and small, non-zero values for an infinite number of other possible, parallel universes. The other universes are expected to have different physical constants than our universe and are believed to be devoid of life.

As seen in the image above, our universe most likely has the greatest value

of the wave function. We are able to exist in our universe because it is

the most probable and most likely to exist.

The problem with Hartle and Hawking's theory is that it predicted the universe is "closed." Consider a closed universe to be the surface of an inflating balloon. Objects such as galaxies on the surface of the balloon would move away in one direction as the balloon inflates, and eventually end up at their initial positions. In addition, the concept of a closed universe implies that the universe will one day stop expanding, and collapse under the force of its own gravity.

Observations suggest that there is insufficient matter in the universe to create enough gravity to recollapse it. In fact, there is evidence predicting the universe to be expanding at a faster rate than the inflationary theory predicts. Thus, observations favor the idea of an "open" universe, a universe that will continue to expand. One way of picturing an open universe is thinking of it as a horse's saddle, which curves up on one side and curves down on the other.

In a saddle-shaped universe, the universe does not close

on itself. Depicted is a triangle laid on the surface of the

universe. The curvature of the universe causes the interior

angles of the triangle to have a sum of less than 180 degrees.