The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [190]
Taking the expansion equations seriously to arbitrarily early times (and for definiteness, imagine that space is spherically shaped), we also see that the two regions would have initially separated more quickly in the standard big bang than in the inflationary model: that’s how they became so much farther apart in the standard big bang compared with their separation in the inflationary theory. In this sense, the inflationary framework involves a period of time during which the rate of separation between these regions is slower than in the usual big bang framework.
Often, in describing inflationary cosmology, the focus is solely on the fantastic increase in expansion speed over the conventional framework, not on a decrease in speed. The difference in description derives from which physical features between the two frameworks one compares. If one compares the trajectories of two regions of a given distance apart in the very early universe, then in the inflationary theory those regions separate much faster than in the standard big bang theory; by today they are also much farther apart in the inflationary theory than in the conventional big bang. But if one considers two regions of a given distance apart today (like the two regions on opposite sides of the night sky upon which we’ve been focused), the description I’ve given is relevant. Namely, at a given moment in time in the very early universe, those regions were much closer together, and had been moving apart much more slowly, in a theory that invokes inflationary expansion as compared with one that doesn’t. The role of inflationary expansion is to make up for the slower start by then propelling those regions apart ever more quickly, ensuring that they arrive at the same location in the sky that they would have in the standard big bang theory.
A fuller treatment of the horizon problem would include a more detailed specification of the conditions from which the inflationary expansion emerges as well as the subsequent processes by which, for example, the cosmic microwave background radiation is produced. But this discussion highlights the essential distinction between accelerated and decelerated expansion.
4. Note that by squeezing the bag, you inject energy into it, and since both mass and energy give rise to the resulting gravitational warpage, the increase in weight will be partially due to the increase in energy. The point, however, is that the increase in pressure itself also contributes to the increase in weight. (Also note that to be precise, we should imagine doing this “experiment” in a vacuum chamber, so we don’t need to consider the buoyant forces due to the air surrounding the bag.) For everyday examples the increase is tiny. However, in astrophysical settings the increase can be significant. In fact, it plays a role in understanding why, in certain situations, stars necessarily collapse to form black holes. Stars generally maintain their equilibrium through a balance between outward-pushing pressure, generated by nuclear processes in the star’s core, and inward-pulling gravity, generated by the star’s mass. As the star exhausts its nuclear fuel, the positive pressure decreases, causing the star to contract. This brings all its constituents closer together and so increases their gravitational attraction. To avoid further contraction, additional outward pressure (what is labeled positive pressure, as in the next paragraph in the text) is needed. But the additional positive pressure itself generates additional attractive gravity and thus makes the need for additional positive pressure all the more urgent. In certain situations, this leads to a spiraling instability and the very thing that the star usually relies upon to counteract the inward pull of gravity—positive pressure—contributes so strongly to that very