# Why is cosmological event horizon closer to us than the particle horizon?

From what I learned, cosmological event horizon is the horizon that moves away from us at/more than the speed of light. And particle horizon is the horizon that particles inside the horizon can have a causal connection with us. It is the maximum distance from which particles could have traveled to the observer in the age of the universe. This simply indicates a contradiction to me. How is it possible that the cosmological event horizon is closer?

• What's your source for the claim that cosmo is closer than particle? – Carl Witthoft May 1 '18 at 16:10
• @CarlWitthoft It's true. – pela May 1 '18 at 16:14
• @pela why though could you please explain? – Benjamin May 1 '18 at 16:15
• @CarlWitthoft youtube.com/watch?v=AwwIFcdUFrE It is from a pbs space time video at 3:35. I would really appreciate it if you can take a look. – Benjamin May 1 '18 at 16:15

The event horizon can be thought of as sort of the opposite. At any time $t$, it is the distance from which we will be able to receive light. If the Universe contained no dark energy, there would be no limit to how distant a galaxy could be and we would still be able to see it — just wait long enough. However, the accelerated expansion means that an increasingly smaller part of the Universe will be able to emit light toward us with us receiving it, before the expansion carries the photons away faster than they can travel toward us.
The following figure from Davis & Lineweaver (2004) may help explain. It show basically three versions of the same thing, namely how the sizes of various horizons evolve with time. The top panel shows time as a function of physical size, while in the middle panel, the $x$ axis show comoving coordinates, i.e. the coordinates that expand along with the Universe. The lower panel shows not time on the $y$ axis, but conformal time, which can be thought of as the time it would take a photon to travel a distance if we "froze" the Universe.