Cosmological horizon
A cosmological horizon is one of two boundaries in three dimensional space, the particle horizon or the event horizon. The particle horizon divides space into those points reached by light traveling to an observer from those points too distant for light to have been observed. The particle horizon is the boundary of the observable universe. The event horizon includes all possible future observations: points outside the event horizon can never be observed. The event horizon is the boundary of all future observable universes. These boundaries are a consequence of general relativity, the expanding universe, and the physics of Big Bang cosmology.
Particle horizon
The particle horizon, also called the comoving particle horizon, is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. It represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe. When cosmologists say "horizon" they almost always mean the particle horizon.In an empty, homogeneous, and isotropic universe the proper distance to the horizon at time is
where is the cosmological scale factor with dimensions of length.
In terms of comoving distance, the particle horizon is equal to the conformal time that has passed since the Big Bang, times the speed of light. In general, the conformal time at a certain time is given in terms of the normalized scale factor by,
The particle horizon is the boundary between two regions at a point at a given time: one region defined by events that have already been observed by an observer, and the other by events which cannot be observed at that time. It represents the furthest distance from which we can retrieve information from the past, and so defines the observable universe.
Event horizon
The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the cosmic event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future. The current distance to our cosmic event horizon is about, well within our observable range given by the particle horizon.In general, the proper distance to the event horizon at time is given by
where is the time-coordinate of the end of the universe, which would be infinite in the case of a universe that expands forever.
For our case, assuming that dark energy is due to a cosmological constant Λ, there will be a minimum Hubble parameter He and a maximum horizon de which is often referred to as the only particle horizon: