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The particle horizon is defined as the maximum distance up to which light can travel between two given times $t_i$ (often taken to be zero with $a(t_i)=0$) and $t$. This is the farthest distance in the sky up to which an observer can communicate, or have information from. This is known as the particle horizon. In other words, the observer and the horizon are causally connected. This horizon is finite because of the finite velocity of light and the finite age of the universe.

What is the definition of the term "causal horizon" and how is it different from the "particle horizon"?

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"Causal horizon" is not a common name I have seen, but indeed there is a clear distinction made by Rindler (1956, MNRAS 116) between "event horizon" and a "particle horizon." Both types of cosmological horizons depends on the observer.

In short, "an event-horizon, for a given observer $A$, is a (hyper-) surface in space-time which divides all events into two non-empty classes: those that have been, are, or will be observable by A, and those that are forever outside A’s possible powers of observation". A "particle horizon", on the other hand, is defined for an observer $A$ and a time $t$, and divides the instantaneous 3-space (from $A$ perspective) in two regions: those which have been observable by $A$ (or which are causally connected with $A$, it is the same thing) and those which have not been.

FRW flat models with (dark & normal) mass but without cosmological constant (or dark energy) have particle horizons, but no cosmological event horizons: the whole universe will become observable given enough time. On the other hand, the $\Lambda$-CDM universe has both type of horizons. An expanding particle horizon, which will only expands until the dark energy dominates completely the cosmological dynamics. From that point on, the universe will expand very rapidly, our particle horizon will contract, and whatever it has not been at any time within our particle horizon will never be: they are beyond our event horizon.

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  • $\begingroup$ Please see this pdg review pdg.lbl.gov/2017/reviews/rpp2017-rev-inflation.pdf It mentions the term "causal horizon" in the first paragraph. @Enredanrestos $\endgroup$ – SRS Mar 7 '18 at 13:12
  • $\begingroup$ In the context of that paragraph, I think "causal horizon" is a synonym of the particle horizon of a comoving point at the time of last scattering. It is clear though that they are not making the distinction I make in my answer. $\endgroup$ – Enredanrestos Mar 8 '18 at 1:01

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