**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 *H*_{0}^{-1} provides a
rough guide for the age of the universe, the Hubble distance
*cH*_{0}^{-1} provides a rough estimate of the
horizon distance in a matter- or radiation-dominated universe.