# I The particle horizon value is ignoring inflation?

1. Jul 20, 2017

### DoobleD

In a paper from 2003, it has been shown that the particle horizon is about 14300 Mpc, or 46.6 billion light years (and it has been recalculated in 2016 with more accurate parameters values at around 14200 Mpc = 46.3 billion ly).

From what I understand, the calculation proposed in 2003 takes the end of inflation as the beginning time. They compute a conformal time η(t) of ther Universe, and they write :

This formula will accurately track the value of η(t), providing that this is interpreted as the value of the conformal time since the end of the inflationary period at the beginning of the universe. (During the inflationary period at the beginning of the universe, the cosmological constant assumed a large value, different from that observed today, and the formula would have to be changed accordingly. So we simply start the clock at the end of the inflationary period where the energy density in the false vacuum [large cosmological constant] is dumped in the form of matter and radiation. Thus, when we trace back to the big bang, we are really tracing back to the end of the inflationary period. After that, the model does behave just like a standard hot-Friedmann big bang model. This standard model might be properly referred to as an inflationary-big bang model, with the inflationary epoch producing the Big Bang explosion at the start.)

They say that the formula they used would have to be changed if they took a starting time prior to the inflation end. So basically my question is : is the particle horizon really around 46 billion ly ? How sure are we if we are ignoring inflation in the cequations ? Would it be (significantly) different if we could compute it from an earlier time ?

During inflation expansion was super fast, so wouldn't that affect today's particle horizon ? I would assume it would make it much larger. We often hear that the (theorically) observable Universe has a radius of around 46 billion ly, and I wonder how valid is this affirmation.

Last edited: Jul 20, 2017
2. Jul 20, 2017

### Staff: Mentor

With inflation, it would be vastly larger (tens of orders of magnitude), but we have no idea how much larger. But no particle would have traveled undisturbed through the inflationary universe, so we cannot really get particles from larger distances, and for many calculations only the expansion after inflation is relevant.

3. Jul 20, 2017

### DoobleD

That answers my question ! Thank you !

4. Jul 20, 2017

### Chronos

Keep in mind the particle horizon represents the maximum distance from which particles could have traveled to the observer in the age of the universe. The time this take is referred to as cosmic time. Given the universe has been expanding since its origin, the particle horizon is more distant than the conformal age of the universe times c. See; https://arxiv.org/abs/1310.6329, A Thousand Problems in Cosmology: Horizons, for further discussion.

5. Jul 20, 2017

### DoobleD

Isn't the particle horizon actually the conformal age of the Universe (which is not the actual age of it) times c ?

EDIT : That's what Wikipedia says, but it could be wrong, the paper from 2003 doesn't seem to treat conformal time that way. Anyway I think I get your point that the particle horizon is not simply the age of the Univers times c, due to expansion.

Last edited: Jul 20, 2017