Problems with the Hot Big Bang

The hot big bang theory has been extremely successful in correlating the observable properties of our Universe, but it has some problems. These difficulties are not so much errors as they are assumptions that are necessary but that do not have a fundamental justification. The required discussion is technical, so we will be content with a rather superficial statement of three basic problems that are associated with the big bang. We shall then consider how these problems might be cured by a new idea that arises from considering the implications of elementary particle physics for cosmology that is called cosmic inflation.

The Horizon Problem

The first difficulty associated with the big bang goes by the name of the horizon problem. We have already encountered the horizon problem in conjunction with the discussion of the cosmic microwave background: when we look at the microwave background radiation coming from widely separated parts of the sky, it can be shown that these regions are too separated to have ever communicated with each other, even with signals traveling at light velocity. How did they "know" to have almost exactly the same temperature? Regions that are too far apart to have ever exchanged light signals are said to be out of causal contact, because one region cannot have caused something to happen in the other since no signals could have been exchanged.

Causally Unconnected Regions
A detailed analysis indicates that the presently observable Universe corresponded to some 100,000 separate causally-unconnected regions at the recombination transition. That is, one could imagine breaking the volume of the Universe at the recombination transition that would expand to become the presently observable Universe into about 100,000 separate regions that would not yet have had time to communicate with each other.

This general difficulty is called the horizon problem, since a limit to having received a signal from some distant source because of the finite speed of light is termed a horizon in cosmology (see the box below). It is a basic fact of big bang cosmology, illustrated in the above right figure, that two points currently outside each other's horizons have always been outside each other's horizons, all the way back to the big bang. Thus, in the standard big bang theory we are forced to assume the required level of uniformity in different parts of the Universe, even if it appears that those parts have never been in causal contact.

Technically Speaking:
More on Horizons
As noted before, horizons result when the finite speed of light sets a limit on how far away an object can be and still get a signal to us in the time since the formation of the Universe. Whether there are horizons depends on the geometry of the Universe.
Many aspects of horizons are conveniently represented in terms of a lightcone diagram, as illustrated in the adjacent figure for the simplified case of two space dimensions (x and y) and one time dimension t (multiplied by c). Recall that the lightcone diagram was introduced in Chapter 2 as part of our discussion of the special theory of relativity.
Particle Horizons: Because the surface of the cone corresponds to travel at light speed, all physical signals that we can observe now are confined to the past lightcone or its interior. Thus, when we consider our position marked "Now" at the intersection of the three axes, the circle marked "Particle Horizon" represents the largest distance from us that a signal source that we have seen could have been at the time marked t = 0 (the beginning of the Universe). Anything at a larger spatial distance than that cannot (yet) be seen by us, since there hasn't been time for light to get here since the beginning of time in the big bang. We say that it lies beyond our (particle) horizon.
Event Horizons: It is sometimes useful to distinguish a second type of horizon that is called an event horizon. We can ask, what is the largest radius for an event that can send a light signal today that we can detect at any time in the future? This is illustrated by the circle marked "Event Horizon". Signals sent from that circle will arrive at our position at the time marked t (max) by following the dashed lines. If that time is the largest possible time in our Universe, the circle drawn at the time "Now" defines the event horizon for our Universe. From the diagram, the event horizon is just the largest possible particle horizon. Event horizons generally don't play as important a role in cosmology as particle horizons, but they are very important for black holes.