Observable Universe - Particle Horizon

Particle Horizon

The particle horizon (also called the cosmological horizon, the light horizon, or the cosmic light horizon) is the maximum distance from which 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. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model being discussed.

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 . The quantity is given by,

where is the scale factor of the Friedmann–Lemaître–Robertson–Walker metric, and we have taken the Big Bang to be at . In other words, the particle horizon recedes constantly as time passes, and the observed fraction of the universe always increases. Since proper distance at a given time is just comoving distance times the scale factor (with comoving distance normally defined to be equal to proper distance at the present time, so at present), the proper distance to the particle horizon at time is given by

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 event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future. At present, this cosmic event horizon is thought to be at a comoving distance of about 46 billion light years. 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.