Difference between hubble sphere,particle horizon and event

[Figaro]

Based on my understanding,

Hubble sphere is the region that contains GALAXIES receding subluminally while GALAXIES outside are receding superluminally (obviously on the border, GALAXIES recede at the speed of light).

Particle horizon is the limit of what we have seen so far since the (big bang? Light scattering? Or the light spectrum reached visible due to redshift?)
*So far I think I understand the Hubble sphere but when particle horizon comes in, I'm confused, so many questions.

Event horizon is the boundary in which future objects can come into causal contact with us, beyond it are things that we can never have any information to.

Questions:
1) The Hubble sphere divides galaxies that recede superluminally and subluminally, so in an accelerating universe like ours, the Hubble sphere should get smaller since galaxies will eventually recede faster than before, is this correct?
2) If the galaxies outside the Hubble sphere are receding superluminally and the Hubble sphere is getting smaller then we can never have any contact with those galaxies, so where is the particle horizon? Same as Hubble sphere? I know they are not the same but I'm confused.

I have read Cosmology by Harrison but I'm confused, there are a lot of clarifications that I need.

 

[haushofer]

Maybe this link helps:

http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

e.g. page 42 below :)

 

[Bandersnatch]

You've got Hubble sphere right.

Particle horizon is the proper distance (i.e. as measured by a meter stick now, with expansion frozen for the time of measuremnt) to what you see NOW as the farthest object - ie. to where the object that emitted the light you now see have been carried by the expansion in the time it took for its light to reach you.

Event horizon is the largest distance at a given time from which light can ever reach you. The difference from your definition is in its time dependence - it grows.

Re.: 1) You can have a growing Hubble sphere in an accelerating universe (as is the case in ours). The acceleration means that the distance to any given galaxy as you trace its progress through time will increase in an accelerated fashion - you can have this happen even if the rate of expansion (i.e. Hubble constant) is going down, as long as the rate of reduction of the expansion rate is low enough.
A good analogy here is the compound interest accumulation on your bank account. Say you've got X amount of money on an account with Y% growth rate. Your savings can grow in an accelerated fashion even if the percentage rate goes down. E.g., if the percentage rate goes down asymptotically to some set value such as in the case if (for example) it is defined as 5+5/{number of months} %: you'll get 10% on the first month, 7.5% on the second, and 5% in the infinite future.
The difference in the rate during the first few months might make your savings grow at a decelarated fashion, but eventually they'll start to accelerate, and in the far future it'll grow exponentially.
X here is the analogy of the scale factor, or proper distance to a test galaxy. Y is the Hubble constant. The far future is equivalent to a DeSitter universe where matter got diluted so much that the expansion is dictated by the cosmological constant only.

2) does not follow then, since the Hubble sphere does grow.

 

[Figaro]

You've got Hubble sphere right.

Particle horizon is the proper distance (i.e. as measured by a meter stick now, with expansion frozen for the time of measuremnt) to what you see NOW as the farthest object - ie. to where the object that emitted the light you now see have been carried by the expansion in the time it took for its light to reach you.

Event horizon is the largest distance at a given time from which light can ever reach you. The difference from your definition is in its time dependence - it grows.

Re.: 1) You can have a growing Hubble sphere in an accelerating universe (as is the case in ours). The acceleration means that the distance to any given galaxy as you trace its progress through time will increase in an accelerated fashion - you can have this happen even if the rate of expansion (i.e. Hubble constant) is going down, as long as the rate of reduction of the expansion rate is low enough.
A good analogy here is the compound interest accumulation on your bank account. Say you've got X amount of money on an account with Y% growth rate. Your savings can grow in an accelerated fashion even if the percentage rate goes down. E.g., if the percentage rate goes down asymptotically to some set value such as in the case if (for example) it is defined as 5+5/{number of months} %: you'll get 10% on the first month, 7.5% on the second, and 5% in the infinite future.
The difference in the rate during the first few months might make your savings grow at a decelarated fashion, but eventually they'll start to accelerate, and in the far future it'll grow exponentially.
X here is the analogy of the scale factor, or proper distance to a test galaxy. Y is the Hubble constant. The far future is equivalent to a DeSitter universe where matter got diluted so much that the expansion is dictated by the cosmological constant only.

2) does not follow then, since the Hubble sphere does grow.

I still don't understand how can the Hubble sphere expand if the galaxies previously receding subluminally, are now receding superluminally, doesn't that mean that more galaxies would recede superluminally leaving lesser galaxies receding subluminally therefore the Hubble surface should contract? Also, in your argument, doesn't 5+5/{number of months} % approach 5 as months approach infinity? So it will have a constant rate therefore no acceleration.

 

[Bandersnatch]

While more and more galaxies are receding superluminaly as time passes, it doesn't follow from this that the Hubble sphere (Hr) should contract. Galaxies will always be leaving Hr as long as Hr does not grow as fast as c.

5% rate in the far future does not mean no acceleration - it means exponential acceleration, just as it means exponential growth of your savings (5% from the previous month's balance).

 

[Figaro]

While more and more galaxies are receding superluminaly as time passes, it doesn't follow from this that the Hubble sphere (Hr) should contract. Galaxies will always be leaving Hr as long as Hr does not grow as fast as c.

5% rate in the far future does not mean no acceleration - it means exponential acceleration, just as it means exponential growth of your savings (5% from the previous month's balance).

How should it not contract? From the definition that the Hubble sphere is the region where subluminal galaxies are and outside are galaxies which are superluminal, isn't it straightforward to say that since the universe is expanding then EVENTUALLY the galaxies receding subluminally will achieve superluminal speeds?

 

[bapowell]

There is an Insights article on this topic: https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[Schneibster]

I'll add a public link to Lineweaver/Davis (2003) which I found quite readable (if a bit of a slog): http://arxiv.org/pdf/astro-ph/0310808v2.pdf

It's good to have both the popular science treatment and the underlying paper, I think.

 

[Jorrie]

How should it not contract? From the definition that the Hubble sphere is the region where subluminal galaxies are and outside are galaxies which are superluminal, isn't it straightforward to say that since the universe is expanding then EVENTUALLY the galaxies receding subluminally will achieve superluminal speeds?

I guess you are thinking in terms of comoving coordinates, where the distance to comoving galaxies remain constant and hence the Hubble radius shrinks in that system of coordinates..
When we are speaking of recession rates, we normally use proper (increasing) distances against cosmological time. Then the Hubble radius grows until it asymptotically reaches a constant value, which depends on the cosmological constant.

 

[Ranku]

While on the topic of horizon, inflation blow up the size of the entire universe beyond the size of the observed universe, i.e. the particle horizon. Is there a 'horizon name' for the size of the entire universe?

 

[timmdeeg]

Which 'horizon name' would you expect for the size of the entire surface of the earth? In other words, what does the term 'horizon' necessarily imply?

 

[bapowell]

While on the topic of horizon, inflation blow up the size of the entire universe beyond the size of the observed universe, i.e. the particle horizon. Is there a 'horizon name' for the size of the entire universe?

I think the amount of expansion, given in terms of the number of e-foldings, is closest to what you want. The particle horizon is the closest thing to defining the edge of the observable universe.