# Horizon Problem

One issue to this entire BIg Bang scenario which has only recently been plausibly explained. At each instant in the history of the Universe, there is a characteristic 'radius' of the Universe which is set by the distance that light could have traveled since the birth of the Universe (recall that light travels at 300,000 kilometers per second for all observers). Thus, if the Universe were only one second old, then an observer cannot see things which are more than 300,000 kilometers away; there has simply not been sufficient time for this light to propagate that far. Since no observer can see beyond this distance, the surface at this distance is also called the 'horizon' for the observer. As the Universe ages, the horizon expands outwards because there is more time for light to travel.

An important side effect is that if we cannot see beyond the horizon, then neither can we be affected by any physical effect from beyond the horizon. Regions of space in the Universe which are separated in distance by more than the horizon simply do not know about each other, and cannot influence each other's physical conditions. If we calculate the size of the horizon in the sky for the Universe at the epoch of decoupling, it turns out to be approximately one degree (about twice the angular diameter of the Moon). The fact that the spectrum and intensity of the CMBR are essentially the same for patches much larger than this size is very hard to explain since our scenario does not allow these patches to communicate with each other and conspire to determine their physical characteristics.

A solution to this dilemma was found in the early 1980's and is called 'inflation' theory. The concept, motivated by a merging of high energy particle physics theory with cosmology, is that within the first 10^-34 seconds of the Big Bang, the Universe went through a period of extremely rapid expansion. This causes our entire Universe to be derived from a very small region of space (before inflation), which would have very uniform properties because it was small and its constituent parts could indeed communicate with each other. Thus, when we observe the CMBR from parts of the sky which are separated by more than one degree, the intensity variations are those imposed by the conditions in the pre-inflationary era (when the Universe was less than 10^-34 seconds old!). After inflation, there is simply no way for physical processes to modify these variations. At angular sizes less than one degree, however, there has been sufficient time for physical interactions to modify the intensity of the CMBR at the epoch of decoupling, and the resulting variations in intensity depend on the details of the theory of such interactions.