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Concept
Particle horizon
Summary
The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. Much like the concept of a terrestrial horizon, 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. Due to the expansion of the universe, it is not simply the age of the universe times the speed of light (approximately 13.8 billion light-years), but rather the speed of light times the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model.
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 by
where is the scale factor of the Friedmann–Lemaître–Robertson–Walker metric, and we have taken the Big Bang to be at . By convention, a subscript 0 indicates "today" so that the conformal time today . Note that the conformal time is not the age of the universe, which is estimated around . Rather, the conformal time is the amount of time it would take a photon to travel from where we are located to the furthest observable distance, provided the universe ceased expanding. As such, is not a physically meaningful time (this much time has not yet actually passed); though, as we will see, the particle horizon with which it is associated is a conceptually meaningful distance.
The particle horizon recedes constantly as time passes and the conformal time grows. As such, the observed size 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
and for today
In this section we consider the FLRW cosmological model.
Official source
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