What is the meaning of the particle horizon in conformal diagrams?

I'm reading "Physical Foundations of Cosmology" (Mukhanov) and in Chapter 2.3 conformal diagrams get introduced. They seem to be a (graphical) tool to understand the causal structure of the universe. In these diagramms two things seem to be important: 1. the particle horizon and 2. the event horizon. I understand the region that is seperated by the event horizon. Stuff inside can not talk to stuff outside of that region. I do not understand what is so special about the particle horizon. I think I can talk to people outside the horizon (while I am inside). If I do not move in space/position (position = comoving distance) than I can leave the particle horizon (if I start inside of it).

I read that the particle horizon is the edge of the observable universe. Since I can leave this region this statement does not make sense to me.

• Hi. Great answer (much better from Wiki). I wonder why no upvotes has come to this question and this answer. Anyway Thanks. – Constantine Black May 28 '16 at 11:11

In short: The particle horizon is the extent of our future light cone at $t=0$, and the event horizon is the extent of our past light cone at $t=\infty$. It is important to be clear that these horizons are horizons only to an observer at this place in Space and Time. They do not mark physical boundaries between different regions in Space; rather, they describe boundaries for regions in Space and Time observable to us, on Earth, at this particular time. An observer somewhere in the Virgo cluster will see different horizons, spherical, at the same distances as we see them, and with themselves in the exact centre.

Particle horizon:

This is the distance from which light emitted at t=0 can have reached us today. In all practicality, this is marked by the Cosmic Microwave Background at a redshift $z \approx 1100$, before which the Universe was opaque, so we cannot see further back when looking at electromagnetic radiation. There is hope, though, that neutrino and Gravitational Wave observatories in the not too far future can push us closer to the $z = \infty$ limit at the Big Bang. The Particle horizon is always expanding, in all cosmological models. In our currently favoured cosmological model, it is around 43 billion light years away.

Event horizon:

This is the distance, inside of which photons emitted in our direction today will reach us in a finite time in the future. When light in distant parts of the Universe is emitted towards us, their journey is a race between their velocity towards us and the cosmological expansion of Space. The expansion of Space is homogeneous, which means that the recession velocity of a region is proportional to its distance. There is a distance, at which the recession velocity equals the speed of light; this is the distance we call the Hubble Sphere. However, in most cosmological models, the Hubble Sphere is not a horizon; it is perfectly possible to observe galaxies that are currently and have always been receding from us at superluminal speed; we have been doing this routinely for decades. This is because even though these photons are initially moving away from us, they are moving into regions of Space which are receding more slowly from us, until the "catch up" with our Hubble Sphere and start approaching us.

However, if the expansion is fast enough, it will "win" over the expansion of the Hubble sphere at some distance. This means that beyond this distance, photons will never get to our Hubble Sphere and thus never reach our telescopes, because the Universe expands so rapidly that the "crawl" towards our cosmic neighbourhood is too slow. Unlike the Particle Horizon, not all cosmological models have an event horizon - but the one which seems to describe our Universe does, and it is at a redshift of around $z\sim 2$.

But... But...

Yes, we routinely observe objects at distances far beyond that of the event horizon. The Event Horizon is a horizon in Time, not only in Space. What we observe at those distances is all in the past, though. As the Universe expands, these objects cross our event horizon at a given time in their history. From Earth, when we look at a galaxy at these distances, we will see the light from this galaxy being increasingly redshifted as we observe epochs closer and closer to this point in time. This also means a slowing down of the perceived time; on top of the increasing redshift, we will see the galaxy's history slow down and grind to a complete halt as we come asymptotically closer to this point in its history - this event - beyond which we can never get more information. We can easily observe galaxies at $z = 2$, but what happens at these galaxies right now, we will never be able to know.

Remember that an event in relativity is a point in Spacetime. the Event Horizon is aptly named - it is not a geometrical horizon made up of points in Space, but made up of events; of points in Spacetime.

• "In our currently favoured cosmological model, it is around 43 billion light years away." When ignoring inflation. – user102008 Jul 12 '16 at 21:30
• @user102008 Inflation happened long before (relatively speaking) the emission of the CMB, so it would not make much sense to not ignore it. – Thriveth Jun 26 '18 at 12:34
• But that statement is not talking about the emission of the CMB, but rather the particle horizon, which is the comoving distance of points whose signal could have reached us since the beginning of time. I believe that any model that can account for the horizon problem (by using inflation or any other way), must allow a signal from a single point to have been able to travel to the CMB at the opposite sides of the sky between the beginning of time and when the CMB was emitted. This would imply that the particle horizon is at least twice the comoving distance to the CMB. – user102008 Jun 26 '18 at 15:18
• In terms of pure GR, I suppose that is true. But in practice, inflation eradicates all signals en route when it sets in. First, Inflation stretches the universe to a factor of $10^{30}$. This means that even extreme hard gamma rays are shifted to AU-scale wavelengths. and even a Planck energy photon ends at energies of nano-eV. Second, the end of Inflation sees the decay of the inflaton field, which releases a flood of super hot photons, vastly outnumbering any relic photons from before. Plus, people are not even convinced the electromagnetic and weak forces had even decoupled yet by then. – Thriveth Jun 26 '18 at 23:24
• Whichever mechanisms would have sent off gravitational waves during the $10^{-36} s$ before Inflation are at least still evading us. Perhaps some exotic effects of entanglement released after Inflation can one day be discovered. But to a very good approximation, the particle horizon distance at the end of inflation is $D_p(t_e) \approx 0$. – Thriveth Jun 26 '18 at 23:32