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result in an explanation of inflation. This achievement is not at all trivial, for string theory, as a consequence of its symmetry principles, deals much more naturally with the opposite situation: negative energy density with positive pressure, rather than positive energy density with negative pressure. Once enough ingredients of string theory, related to what is going on in its extra dimensions, became understood, researchers were able to start constructing configurations able to account for the inflation of a universe. Finally completed by Renata Kallosh, Shamit Kachru, Andrei Linde, and Sandip Trivedi, such models were subsequently studied by many others. But in these or other scenarios, the constructions appear too contrived and not restrictive enough to provide clear predictions regarding inflation. In loop quantum cosmology, any inflationary effects would be a consequence of its basic properties, the atomic nature of space and time. Although the number of possibilities is smaller, it is still not small enough here to suggest clear test conditions for cosmological observations. Specific aspects will be discussed later in this chapter and in chapter 8.

So far, inflationary behavior of the early universe has been considered mainly in the context of more traditional questions in cosmology, in particular to explain how the large-scale structures we see now could have arisen. To see the role of the proposal of inflation, we first indicate what cosmology would be like if no inflationary episode had happened. Cosmic background radiation allows one to draw conclusions about early matter with its near but not exact homogeneity. Fine structures in this heavenly intensity distribution can be computationally evolved to earlier times by letting Einstein’s equations run backward. In this backward evolution, the distribution becomes more and more homogeneous—which is not surprising, since it is understood as an indication of gravitational clumping building up in time. The earlier in the big bang phase we are, the more homogeneous the universe is. This looks attractive, for it indicates that our complex universe could have emerged from a very simple initial state. Only the reigning gravitational attraction of matter in an expanding universe would have led to all the complicated structures we can now see, in gigantic accumulations of galaxies all the way down to our solar system and the planets. A simple initial state suggests that we could one day, in an ultimate explanation, infer the reason for our own universe and answer the fundamental questions: Why is it as it is, and why is it at all?

Alas, a very homogeneous initial state in the early universe may present a severe problem for the consistency of cosmology. Viewing the universe with its big bang singularity as a starting point, there is a finite maximal duration for the propagation of signals between two points: If a signal starts at the singularity (or shortly thereafter, since all theory breaks down at the singularity itself), it can travel only a certain distance to some other point at a later time. Using the known speed of light, the largest distance can be computed in general relativity, and it is so small that normal circumstances would not allow light signals in the early universe to traverse all space. Here lies the problem—the horizon problem—for how could a homogeneous distribution, with equal densities everywhere, have come about if no signals could have controlled this homogeneity?

At this point inflation enters the game, because the mentioned “normal circumstances” include positive pressure as one condition. With negative pressure active for sufficiently long, on the other hand, it is, as Guth noted, very easy for signals to communicate between all possible places in the early universe. The rapid expansion of space-time would carry along all signals, allowing them to reach much farther distances not by their own motion but by surfing on the accelerating universe. No consistency problem exists in an inflationary universe, which is one of the attractions of the