Particle Horizon of The Observable Universe
The particle horizon of the observable universe is the boundary that represents the maximum distance at which events can currently be observed. For events beyond that distance, light has not had time to reach our location, even if it were emitted at the time the universe began. How the particle horizon changes with time depends on the nature of the expansion of the universe. If the expansion has certain characteristics, there are parts of the universe that will never be observable, no matter how long the observer waits for light from those regions to arrive. The boundary past which events cannot ever be observed is an event horizon, and it represents the maximum extent of the particle horizon.
The criterion for determining whether an event horizon for the universe exists is as follows. Define a comoving distance by
In this equation, a is the scale factor, c is the speed of light, and t0 is the age of the universe. If (i.e. points arbitrarily as far away as can be observed), then no event horizon exists. If, a horizon is present.
Examples of cosmological models without an event horizon are universes dominated by matter or by radiation. An example of a cosmological model with an event horizon is a universe dominated by the cosmological constant (a de Sitter universe).
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