### Why is there a difference between the cosmic event horizon and the age of the universe?

• According to wiki the cosmic event horizon is 5 Gpc but the age of the universe is about 13,7 billion years. Usually light from far galaxys needed at most 13,7 billion years to reach the earth so the event horizon should be the same. But in wiki the event horizon is 5*3,2billionly=16 billion ly. So is this difference just a matter of rounding or old data or is there something else what causes the differences?

https://en.wikipedia.org/wiki/Cosmological_horizon#Event_horizon

• pela Correct answer

6 years ago

From the link you provide:

The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future. The current distance to our cosmic event horizon is about 5 Gpc, well within our observable range given by the particle horizon.

Your confusion somes from the fact that you are mixing to different horizons:

The particle horizon is the sphere centered on us that has a radius equal to the distance that light can travel in 13.8 Gyr (the age of the Universe). That is, light that was emitted when the Universe was born at a point on that horizon, reaches us today. Note that, because the Universe is expanding, the distance is not 13.8 Glyr, or 4.2 Gpc, as one might naively expect, but in fact 46.3 Glyr.

The cosmic event horizon is also a sphere centered on us, which is the boundary inside which light, if it is emitted today, may still reach us sometime in the future. If it is emitted outside this horizon, the expansion of the Universe ensures that the light will never reach us.

As time goes, we will see light that came from farther and farther away, and thus the distance to the particle horizon is increasing. Meanwhile, the accelerated expansion of the Universe ensures that light emitted from distant galaxies in the future are able to reach us only if they are increasingly closer. Thus fewer and fewer galaxies will be inside the event horizon. But since space is at the same time expanding, the boundary will asymptotically reach a finite size (~17 Glyr).

You can see the particle and the event horizons as blue and red lines in the plot in @Pulsar's great answer here.

The 16.5 Glyr that the distance to the event horizon is today is sort of a coincidence. It has nothing to do with the age of the Universe. It only depends on the future expansion of the Universe, which in turn depends on the densities of the components of the Universe ($$\Omega_\mathrm{b},\Omega_\mathrm{DM},\Omega_\Lambda$$, etc.). If the Universe had been dominated by matter (or radiation), then there would be no event horizon: No galaxy, ever-so far away would not be visible to us, if we just had the patience to wait. A galaxy is 10,000 billion lightyears away? Just wait long enough (exactly how long depends on the actual density).

However, our Universe happens to be dominated by dark energy, which accelerates the expansion without boundaries. This unfortunately means that the light leaving today from a galaxy 17 Glyr away will be carried away by the expansion faster than it can travel toward us. In contrast, the light emitted today from a galaxy 15 Glyr away will travel in our direction, but will nonetheless initially move away from us due to the expansion. However, its journey toward us makes this expansion rate smaller and smaller (since the expansion rate increases with distance from us), and after a period of time it will have traveled so far that it has overcome expansion and starts decreasing its distance from us and eventually reach us after 100 Gyr or so.

Do you know how they get to 16 billion ly?

@Marijn: Yes, that's the solution to the equation given in your link, using $t_\mathrm{max} = \infty$ since the Universe will expand forever.

I'm not very good in understanding that formula can you perhaps explain in simple words why it is zo close to the age of the universe but still is a bit more?

@Marijn: See my edit in a minute.

If I got it right, shouldn't be the event horizon simply $\frac{c}{H_0}$? This would give the distance at which the expansion of the universe becomes faster than the speed of light. Or doesn't it?

@t.rathjen: The expansion being faster than light is not a problem. The event horizon has always been moving away from us at $v>c$, but does asymptotically go toward being the distance at which $v=c$. This distance decreases toward zero.