# 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? Commented May 1, 2018 at 16:10
• @CarlWitthoft It's true.
– pela
Commented May 1, 2018 at 16:14
• @pela why though could you please explain? Commented May 1, 2018 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. Commented May 1, 2018 at 16:15

The particle horizon marks the region from within which we may have received light. It started out at zero, because light from nowhere had had the time to reach us, and increased as time went by because light from increasingly larger distance reached us. Due to the expansion it will always increase in physical size, but due to the accelerated expansion, there is a limit to the region of the Universe that we will ever be able to receive light from. Today, the particle horizon is 46 Glyr (billion lightyears) away, and the limit — in the far future — is the part that today is 63 Glyr away (but in the far future will be much farther away).

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.

At Big Bang, the event horizon consisted of particles that today are 63 Glyr away — that's what I meant by "the opposite of the particle horizon".

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.

• Are my definitions of the two horizons incorrect? Commented May 1, 2018 at 16:55
• So, basically, at some particular time in the future, the two horizons will cross? Commented May 1, 2018 at 16:57
• @CarlWitthoft They already did that, when the Universe was ~4 Gyr old.
– pela
Commented May 1, 2018 at 17:17
• @Edouard Yes, by "freezing the Universe" I meant "magically stop the expansion in a way that would still let photons travel through it at the speed of light". I'm unsure what you mean by the last part though?
– pela
Commented Oct 15, 2021 at 21:53
• @Edouard Hmm… I'm not sure the Poincaré recurrence applies to our Universe as a whole, but this is beyond my knowledge. What I tried to say is that the conformal time is the distance in Glyr, divided by the speed of light. That means that it's the time it would take a photon to travel that distance, if it wasn't for expansion.
– pela
Commented Oct 16, 2021 at 8:40