2.5. Horizons
One of the most crucial concepts to master about FRW models is the existence of horizons. This concept will prove useful in a variety of places in these lectures, but most importantly in understanding the shortcomings of what we are terming the standard cosmology.
Suppose an emitter, e, sends a light signal to an observer, o, who is at r = 0. Setting = constant and = constant and working in conformal time, for such radial null rays we have o - = r. In particular this means that
(46) |
Now suppose e is bounded below by e; for example, e might represent the Big Bang singularity. Then there exists a maximum distance to which the observer can see, known as the particle horizon distance, given by
(47) |
The physical meaning of this is illustrated in figure 2.3.
Similarly, suppose o is bounded above by o. Then there exists a limit to spacetime events which can be influenced by the emitter. This limit is known as the event horizon distance, given by
(48) |
with physical meaning illustrated in figure 2.4.
These horizon distances may be converted to proper horizon distances at cosmic time t, for example
(49) |
Just as the Hubble time H0-1 provides a rough guide for the age of the universe, the Hubble distance cH0-1 provides a rough estimate of the horizon distance in a matter- or radiation-dominated universe.