A handful of sand lands on the table. The grains settle in different ways, but if the handful is large, the total volume barely changes. That's roughly how classical gravity works: space appears smooth and definite. But look closely at the individual grains, and you'll find that at the quantum level, volume itself is no longer fixed. It becomes a random variable, one for which you can compute probabilities.
The authors took known formulas for the expansion of the universe and recast them in the language of probabilities. Instead of asking "what is the volume?", they asked: "what is the probability that the volume turns out to be this or that?" They ran the calculations for several approximations, from a crude classical one to an exact quantum treatment in two dimensions. In the classical case, the probability is concentrated around a single value — the one we actually observe. But the more quantum corrections kick in, the more the peak smears out. In the extreme quantum regime, the distribution starts to favor tiny universes.
This is like a lottery where tickets with large numbers win often, as long as the rules are classical. But change the rules, and the winnings shift to tickets with tiny numbers. So it is here: the familiar large cosmos is just the most likely outcome in a world of weak quantum effects. Crank them up, and a universe the size of a pea becomes the more probable bet.
In two dimensions, the calculations were carried through to an exact answer using mathematics that grew out of string theory. There, too, quantum effects turn out to prefer smaller universes.
In the novel "Mr. Tompkins in Wonderland," George Gamow sent his hero to a world where quantum effects are visible to the naked eye. There, the volume of a room could change from one breath to the next — much like in this work.