for the interested reader let me elaborate here in a little more detail. First the problem, again: Consider two regions in the night sky that are so distant from one another that they have never communicated. And to be concrete, let’s say each region has an observer who controls a thermostat that sets his or her region’s temperature. The observers want the two regions to have the same temperature, but because the observers have been unable to communicate, they don’t know how to set their respective thermostats. The natural thought is that since billions of years ago the observers were much closer, it would have been easy for them, way back then, to have communicated and thus to have ensured the two regions had equal temperatures. However, as noted in the main text, in the standard big bang theory this reasoning fails. Here’s more detail on why. In the standard big bang theory, the universe is expanding, but because of gravity’s attractive pull, the rate of expansion slows over time. It’s much like what happens when you toss a ball in the air. During its ascent it first moves away from you quickly, but because of the tug of earth’s gravity, it steadily slows. The slowing down of spatial expansion has a profound effect. I’ll use the tossed ball analogy to explain the essential idea. Imagine a ball that undergoes, say, a six second ascent. Since it initially travels quickly (as it leaves your hand), it might cover the first half of the journey in only two seconds, but due to its diminishing speed it takes four more seconds to cover the second half of the journey. At the halfway point in time, three seconds, it was thus beyond the halfway mark in distance. Similarly, with spatial expansion that slows over time: at the halfway point in cosmic history, our two observers would be separated by more than half their current distance. Think about what this means. The two observers would be closer together, but they would find it harder—not easier—to have communicated. Signals one observer sends would have half the time to reach the other, but the distance the signals would need to traverse is more than half of what it is today. Being allotted half the time to communicate across more than half their current separation only makes communication more difficult.
The distance between objects is thus only one consideration when analyzing their ability to influence each other. The other essential consideration is the amount of time that’s elapsed since the big bang, as this constrains how far any purported influence could have traveled. In the standard big bang, although everything was indeed closer in the past, the universe was also expanding more quickly, resulting in less time, proportionally speaking, for influences to be exerted.
The resolution offered by inflationary cosmology is to insert a phase in the earliest moments of cosmic history in which the expansion rate of space doesn’t decrease like the speed of the ball tossed upwards; instead, the spatial expansion starts out slow and then continually picks up speed: the expansion accelerates. By the same reasoning we just followed, at the halfway point of such an inflationary phase our two observers will be separated by less than half their distance at the end of that phase. And being allotted half the time to communicate across less than half the distance means it is easier at earlier times for them to communicate. More generally, at ever earlier times, accelerated expansion means there is more time, proportionally speaking—not less—for influences to be exerted. This would have allowed today’s distant regions to have easily communicated in the early universe, explaining the common temperature they now have.
Because the accelerated expansion results in a much greater total spatial expansion of space than in the standard big bang theory, the two regions would have been much closer together at the onset of inflation than at a comparable moment in the standard big bang theory. This size disparity in the very early universe is an equivalent way of understanding why communication between