I haven't read the book.
But one of the theoretical developments Hawking is known for was finding a certain mathematical solution that might be interpreted as governing the creation of a universe from nothing (this interpretation is problematic for several good reasoms, but never mind). The universe that gets created is spatially closed; that is, at any given time it has finite volume and the topology of a 3-sphere (a "hypersphere").
It turns out that according to general relativity, the total energy of such a universe is always exactly zero. Crudely speaking the negative gravitational potential energy cancels the positive energy in matter and radiation.
Why? Well, remember that gravitational potential energy is always negative - or to be more precise, it's always monotonically decreasing as you move in from infinity - because gravity is attractive. But on a sphere (and think of the surface of the sphere, not its interior) there is no infinity. The farthest away you can get is the antipode. Work through the math, and you discover that this forces the energy to always sum up to zero.
It's very similar to the reason that the net charge on such a space must always be zero. The flux lines have no infinity to escape to.