Cosmology

On a large scale our universe appears to show a uniform expansion that makes progressively more distant galaxies recede from us at progressively higher speeds. In general relativity this is explained by saying that the initial conditions must have involved expansion—and that there is not enough in the way of matter or gravitational fields to produce the gravity to slow down this expansion too much. (Note that as soon as objects get gravitationally bound—like galaxies in clusters—there is no longer expansion between them.) The standard big bang model assumes that the universe starts with matter at what is in effect an arbitrarily high temperature. One issue much discussed in cosmology since the late 1970s is how the universe manages to be so uniform. Thermal equilibrium should eventually lead to uniformity—but different parts of the universe cannot come to equilibrium until there has at least been time for effects to propagate between them. Yet there seems for example to be overall uniformity in what we see if we look in opposite directions in the sky—even though extrapolating from the current rate of expansion there has not been enough time since the beginning of the universe for anything to propagate from one side to the other. But starting in the early 1980s it has been popular to think that early in its history the universe must have undergone a period of exponential expansion or so-called inflation. And what this would do is to take just a tiny region and make it large enough to correspond to everything we can now see in the universe. But the point is that a sufficiently tiny region will have had time to come to thermal equilibrium—and so will be approximately uniform, just as the cosmic microwave background is now observed to be. The actual process of inflation is usually assumed to reflect some form of phase transition associated with decreasing temperature of matter in the universe. Most often it is assumed that in the present universe a delicate balance must exist between energy density from a background Higgs field (see page 1047) and a cosmological term in the Einstein equations (see page 1052). But above a critical temperature thermal fluctuations should prevent the background from forming—leading to at least some period in which the universe is dominated by a cosmological term which yields exponential expansion. There tend to be various detailed problems with this scenario, but at least with a sufficiently complicated setup it seems possible to get results that are consistent with observations made so far.

In the context of the discoveries in this book, my expectation is that the universe started from a simple small network, then progressively added more and more nodes as it evolved, until eventually on a large scale something corresponding to 4D spacetime emerged. And with this setup, the observed uniformity of the universe becomes much less surprising. Intrinsic randomness generation always tends to lead to a certain uniformity in networks. But the crucial point is that this will not take long to happen throughout any network if it is appropriately connected. Traditional models tend to assume that there are ultimately a fixed number of spacetime dimensions in the universe. And with this assumption it is inevitable that if the universe in a sense expands at the speed of light, then regions on opposite sides of it can essentially never share any common history. But in a network model the situation is different. The causal network always captures what happens. And in a case like page 518—with spacetime always effectively having a fixed finite dimension—points that are a distance t apart tend to have common ancestors only at least t steps back. But in a case like (a) on page 514—where spacetime has the structure of an exponentially growing tree—points a distance t apart typically have common ancestors just Log[t] steps back. And in fact many kinds of causal networks—say associated with early randomly connected space networks—will inevitably yield common ancestors for distant parts of the universe. (Note that such phenomena presumably occur at around the Planck scale of 10¹⁹ GeV rather than at the 10¹⁵ GeV or lower scale normally discussed in connection with inflation. They can to some extent be captured in general relativity by imagining an effective spacetime dimension that is initially infinite, then gradually decreases to 4.)