B What is the reason for galaxies fading in the distant future?

[PeroK]

They mean \ddot{a}>0, which is equivalent to q<0. It turns out that constant H gives \ddot{a}>0. Can you see why?

Yes, but they are not equivalent. Constant $H$ is $q = -1$ whereas $q < 0$ is equivalent to $H' > - H^2$. For constant $q \ne -1$ I get:

$H(t) = [(q+1)t + 1/H_0]^{-1}$ which goes to $0$ as $t \rightarrow \infty$ (for $q > -1$)

And:

$d_{H, com} = \frac{C}{H_0}[H_0(q+1)t + 1]^{\frac{q}{q+1}}$

Which goes to $0$ as $t \rightarrow \infty$ for $-1 < q < 0$.

So, that would be a solution where eventually there is no expansion in terms of $H$ but the comoving Hubble radius has eventually reduced to 0, hence everything not gravitationally bound is gone!

If I've understood your article, then that's the point of $q$. It determines the long-term behaviour of the comoving Hubble radius, hence whether eventually everything is gone ($q < 0$), or eventually everything comes back into the observable universe ($q > 0$).

 

[Flatland]

I'd like to expand on this question a little bit.When another galaxy that is currently receding away from us at greater than c, would there be a point in space where the photons would reach where this other galaxy is receding exactly at c? And if yes would it be possible to be at rest relative to these photons?

 

[bapowell]

I'd like to expand on this question a little bit. What happens when another galaxy that is currently receding away from us at greater than c; would there be a point in space where the photons would reach where this other galaxy is receding exactly at c?

Yes. Since photons from this galaxy eventually reach earth, they must pass a point that is receding from the galaxy at speed c.

 

[Einstein's Cat]

After the cosmological horizon, there is no known mechanism for light to reach us.
The "fading", as explained above, is the real fact that fewer photons reach us ... no amount of detector sensitivity can change that.

How long would it take a typical galaxy to fade away so that it is no longer visible where when t is zero the recessional velocity of the galaxy is c from the perspective of an observer on earth? The means of viewing of the observer is irrelevant.

Is there any data on such a subject? I've looked online and created a thread but to no success.

 

[sunrah]

How long would it take a typical galaxy to fade away so that it is no longer visible where when t is zero the recessional velocity of the galaxy is c from the perspective of an observer on earth? The means of viewing of the observer is irrelevant.

Is there any data on such a subject? I've looked online and created a thread but to no success.

Any answer to the question you ask depends on your cosmological model. Our universe is accelerating, this means that the Hubble parameter is not constant. That is essentially why we can still see objects outside the Hubble radius
<br /> d_{H} = \frac{c}{H_{0}}<br />
where H_{0} is the value of the Hubble parameter at the present time. If the Hubble parameter were constant, the Hubble radius (~14 billion light years) would correspond to the size of the visible universe and the time required for light to reach us from this boundary would be the age of the universe (~14 billion years). As it is the size of the visible universe is much greater ~47 billion light years. The reason we see these regions is because how the value of the scale factor, which describes the expansion of our universe, has changed until the present day. If our universe were to stop expanding suddenly, light from the particle horizon region would take about 47 billion years to reach us, but of course galaxies located inside the particle horizon would not "fade", because the universe had ceased expanding.

What you call fading is galaxies leaving the particle horizon, that is crossing the boundary of the visible universe, due to cosmic (accelerated) expansion. The time t required for a galaxy to leave the particle horizon from time t₀ where v(t₀)=c, depends on the evolution of the scale factor (and therefore Hubble parameter) in the future. This evolution is described by cosmological models like the concordance model. Also, I think standard version of Hubble law needs to be modified as this only applies to low redshift values, i.e. z<<1.

What you really need to understand is that Hubble radius is not a physical boundary - it doesn't really mean much in our particular universe. The particle horizon is the important one. And we can see high redshift galaxies due to the evolution history of our universe. As the universe expands galaxies will leave the particle horizon, eventually all that we will be able to see is our local group of galaxies.

 

[Einstein's Cat]

Any answer to the question you ask depends on your cosmological model. Our universe is accelerating, this means that the Hubble parameter is not constant. That is essentially why we can still see objects outside the Hubble radius
<br /> d_{H} = \frac{c}{H_{0}}<br />
where H_{0} is the value of the Hubble parameter at the present time. If the Hubble parameter were constant, the Hubble radius (~14 billion light years) would correspond to the size of the visible universe and the time required for light to reach us from this boundary would be the age of the universe (~14 billion years). As it is the size of the visible universe is much greater ~47 billion light years. The reason we see these regions is because how the value of the scale factor, which describes the expansion of our universe, has changed until the present day. If our universe were to stop expanding suddenly, light from the particle horizon region would take about 47 billion years to reach us, but of course galaxies located inside the particle horizon would not "fade", because the universe had ceased expanding.

What you call fading is galaxies leaving the particle horizon, that is crossing the boundary of the visible universe, due to cosmic (accelerated) expansion. The time t required for a galaxy to leave the particle horizon from time t₀ where v(t₀)=c, depends on the evolution of the scale factor (and therefore Hubble parameter) in the future. This evolution is described by cosmological models like the concordance model. Also, I think standard version of Hubble law needs to be modified as this only applies to low redshift values, i.e. z<<1.

What you really need to understand is that Hubble radius is not a physical boundary - it doesn't really mean much in our particular universe. The particle horizon is the important one. And we can see high redshift galaxies due to the evolution history of our universe. As the universe expands galaxies will leave the particle horizon, eventually all that we will be able to see is our local group of galaxies.

Thank you for your help; is there an equation that describes how H changes with time?
Also does it take longer for larger galaxies to leave the particle boundary? And why does the time taken for galaxies to leave the particle boundary vary?

 

[sunrah]

is there an equation that describes how H changes with time?

Yes, this is the famous Friedmann equation: https://en.wikipedia.org/wiki/Friedmann_equations

This is the foundation of modern cosmology. To solve it, you must assume a world model. The standard cosmology is the concordance model. if your really interested in learning this and have some physics knowledge I suggest "An Introduction to Modern Comology" by Andrew Liddle. It explains things pretty well.

does it take longer for larger galaxies to leave the particle boundary?

It shouldn't. The motion of the galaxies that we're concerned with here is not peculiar, hmm that is the galaxies aren't actually moving - it is the expansion of intergalactic space that is accelerating therefore you shouldn't need to consider things like inertial mass.

why does the time taken for galaxies to leave the particle boundary vary?

Again it is the expansion that cause recession velocity, therefore the expansion, which is governed by the scale factor, depends on the time-evolution of the scale factor. The Hubble parameter also depends on the scale factor. The scale factor evolves differently in different world models.

 

[Einstein's Cat]

Yes, this is the famous Friedmann equation: https://en.wikipedia.org/wiki/Friedmann_equations

This is the foundation of modern cosmology. To solve it, you must assume a world model. The standard cosmology is the concordance model. if your really interested in learning this and have some physics knowledge I suggest "An Introduction to Modern Comology" by Andrew Liddle. It explains things pretty well.It shouldn't. The motion of the galaxies that we're concerned with here is not peculiar, hmm that is the galaxies aren't actually moving - it is the expansion of intergalactic space that is accelerating therefore you shouldn't need to consider things like inertial mass.Again it is the expansion that cause recession velocity, therefore the expansion, which is governed by the scale factor, depends on the time-evolution of the scale factor. The Hubble parameter also depends on the scale factor. The scale factor evolves differently in different world models.

Apologises for the lack of clarity, but when I meant a larger galaxy, I meant a galaxy with a larger radius; would it take longer to fade away as surely a galaxy of half the radius would pass the boundary quicker?

 

[Jorrie]

Sunrah, there are a few inaccuracies in your statements, e.g.

Our universe is accelerating, this means that the Hubble parameter is not constant.

Actually, a constant Hubble parameter is the sign of an accelerating universe. A non-accelerating universe needs the Hubble parameter to decrease until it vanishes as time goes on.

If the Hubble parameter were constant, the Hubble radius (~14 billion light years) would correspond to the size of the visible universe and the time required for light to reach us from this boundary would be the age of the universe (~14 billion years).

No, I think you are mixing up the Hubble radius, the particle horizon (observable universe radius) and the cosmological event horizon (communications radius). They presently all have different proper distance values and only the Hubble radius and the cosmological horizon will eventually end up the same and constant at around 17 billion light years. The particle horizon will increase without limit.
In the graph below, R is the Hubble radius, D_Hor the cosmological horizon and D_par(ticle) the radius of the observable universe.

In the light of this, please reconsider your response to Einstein's Cat.