What Equation Determines the Cosmic Event Horizon Distance?

[Jay B]

TL;DR Summary

I'm trying to calculate the distance of the cosmic event horizon at different times following the big bang.

Hi Everyone,

I'm hoping someone can share an equation that would give the distance of the cosmic event horizon for a given time after the big bang. Thanks for any help!

Jay

 

[pinball1970]

Summary: I'm trying to calculate the distance of the cosmic event horizon at different times following the big bang.

Hi Everyone,

I'm hoping someone can share an equation that would give the distance of the cosmic event horizon for a given time after the big bang. Thanks for any help!

Before the cosmology guys get here, can you explain what you mean by the phrase 'cosmic event horizon?'

 

[berkeman]

Summary: I'm trying to calculate the distance of the cosmic event horizon at different times following the big bang.

I'm hoping someone can share an equation that would give the distance of the cosmic event horizon for a given time after the big bang.

https://www.physicsforums.com/insights/big-bang-happen/

 

[Ibix]

Equation 28 in Davis and Lineweaver
https://arxiv.org/abs/astro-ph/0310808

 

[Jay B]

Before the cosmology guys get here, can you explain what you mean by the phrase 'cosmic event horizon?'

The distance past which light emitted today would never be able reach us because the expansion of space between Earth and that sphere is expanding faster than the speed of light (or will be).

 

[Jay B]

Equation 28 in Davis and Lineweaver
https://arxiv.org/abs/astro-ph/0310808

Thanks for the link! I'm having a little bit of a hard time working through the equations, but I'll keep at it.

 

[Jay B]

I've seen this diagram on a few sites.

I went down this rabbit hole while watching a video about Mach's principal. It showed the following equation for the gravitational constant: G ≈ c^2 * radius of the universe / mass of the universe. I've always been interested in G, so I fiddled with it a bit. I used the current estimate of the cosmic event horizon to calculate a mass for the universe of about 2.01 * 10^53 kg, which is pretty close to the estimates I've seen. I figured that event horizon was the correct number to use since that would also be the distance beyond which there could be no gravitational interactions. I did go back and forth about if the event or particle horizon would be most appropriate, and I may well have chosen incorrectly.

Since the event horizon (Radius) has changed over time, this would necessitate that at least one other term is variable if the equation is to hold true meaning either G, c, or the mass of the universe has changed over time (or that I'm completely misunderstanding what I'm looking at). I'd be interested to hear how anyone else would interpret this.

 

[Bandersnatch]

It should be the observable universe, so particle horizon and the mass within. You want all the things causally connected at present. Event horizons are about the extreme future.

The nuts and bolts of the Mach's principle are over my head, so I don't know what it does or doesn't imply about any constants.

Btw, it's not generally true that the event horizon is associated with recession velocities exceeding c. See Fig.1 in that paper from post #4. The latter is designated 'Hubble sphere' on those graphs. It coincides with the former only when the acceleration is exponential.