Present distance to surface of transluminal expansion

[yogi]

Is it true for a q = 0 universe, the now (proper)distance to the surface of superluminal recession is approximately double the Hubble scale. If so, if q = -1 what is the approximate distance to the present surface of superluminal recession?

Thanks

 

[marcus]

Is it true for a q = 0 universe, the now (proper)distance to the surface of superluminal recession is approximately double the Hubble scale?...

Yogi, I thought that the Hubble scale was defined to be the current (proper) distance to where recession rate equals c, and so beyond that it exceeds c.

I want to be sure I understand what you mean by the "surface of superluminal recession".

I think that would be where the recession rate of a stationary observer is equal to c. So you just have to solve the Hubble law equation (which uses the now distance---today's proper)

c = Hd
where H is the current Hubble parameter
so therefore d = c/H, which is the Hubble scale, or Hubble distance.

There is this other concept, that of the cosmological horizon. In a non-accelerating universe it does not exist---think of it as infinite. But in an accelerating universe it is the current (proper) distance of a galaxy which, if you left today and traveled towards it at speed c, you would never quite reach. Closer galaxies you could eventually reach traveling at c. A galaxy which is out beyond the cosmological horizon could not today send us a message. Although we see many such galaxies, in fact most visible galaxies are now out beyond the cosmo horizon. I think that distance is roughly 16 billion lightyears proper.

The Hubble distance---which you asked about, is 13-some billion lightyears.

 

[yogi]

Thanks Marcus - I guess I am playing a mind game with myself - its sort of analogous to resolving the difference between the world map and the world picture - if we assume a photon has arrived today from a distance of 13 billion light years - and the source was receding at the time of emission at near c - do we know whether that source is now receding at a speed greater than c or whether it is still receding at near c but it is now at a distance of 26 billion light years, or something inbetween. Since redshift is a relationship between distances and not velocities, it seems there is not enough info to make an absolute conclusion.

 

[yogi]

Comment on my post #3 - ok - If the photon travel time is 13 billion years then the present distance to the source is c/H
I see my error

Thanks Marcus

 

[marcus]

Thanks Marcus - I guess I am playing a mind game with myself - its sort of analogous to resolving the difference between the world map and the world picture - if we assume a photon has arrived today from a distance of 13 billion light years - and the source was receding at the time of emission at near c - do we know whether that source is now receding at a speed greater than c or whether it is still receding at near c but it is now at a distance of 26 billion light years, or something inbetween. Since redshift is a relationship between distances and not velocities, it seems there is not enough info to make an absolute conclusion.

In cosmology essentially all the distance estimates and distance expansion rate estimates that you hear are based on a simple differential equation model called Friedman equations, sometimes spelled double-n Friedmann. You can look up "Friedman equations" on wikipedia.
It's not necessary to look at the equations or to know how to solve them---they are built in to various online calculators. So playing around with Ned Wright's calculator or with Morgan's "cosmos calculator" is equivalent to playing around with the differential equations.

You should try Morgan's, because it gives recession rates, and it gives distance then and distance now. It's user friendly. You put in some redshift you are interested in, like 1.5 or 2 or 6, and it tells you all these things about the galaxy whose light is coming in with that redshift.

I have Morgan's URL in my sig, but you can get it by googling "cosmos calculator" or "Morgan cosmos calculator".

Nothing in science is 100% certain but Friedman (and thus also Morgan's calculator) has a lot of credibility because the Einstein Gen Rel equation has been well tested and because Friedman is just a simplified version of the Einstein equation. Simplified by assuming the universe has no distinguished special point or direction.

When you go to Morgan's calculator you have to prime it by putting numbers in 3 boxes.

Put .27 in the "matter" box
Put .73 in the cosmological constant, or "lambda" box.
Put 71 into the "Hubble" box.

These correspond to parameters which have been measured---for the matter fraction, and the dark energy fraction, and the current Hubble rate. Somebody else might say .25, and .75, and 74. It doesn't make much difference if you make a slight change in the 3 basic parameters.

Then you are ready to go, and you put in a redshift and see what recession speeds and distances correspond.

If you have any trouble, or find something confusing, ask here!

I cosmology I think there is nothing so important as hands-on experience with the standard cosmo model. Please give it a go and tell me what you think.

 

[marcus]

Thanks Marcus - I guess I am playing a mind game with myself - its sort of analogous to resolving the difference between the world map and the world picture - if we assume a photon has arrived today from a distance of 13 billion light years - and the source was receding at the time of emission at near c - do we know whether that source is now receding at a speed greater than c or whether it is still receding at near c but it is now at a distance of 26 billion light years, or something inbetween. Since redshift is a relationship between distances and not velocities, it seems there is not enough info to make an absolute conclusion.

Comment on my post #3 - ok - If the photon travel time is 13 billion years then the present distance to the source is c/H
I see my error

Be careful not to confuse proper distance with light travel time. Proper distance today means the actual distance you would measure if you could freeze expansion today.

If there is some galaxy that is 13 billion lightyears from us TODAY that means if you freeze expansion it would take 13 billion years to send a flash of light to them.

As it happens we are today getting light from that galaxy which (the calculator will show you) is redshifted by z = 1.4.
The calculator will tell you how far that galaxy WAS from us when it emitted the light which we are now getting. Obviously it was much closer than 13 billion lightyears (proper).

The calculator will tell you what the light travel time was. And it will tell you how rapidly the galaxy was receding when it emitted the light. And it will tell you its recession rate TODAY. Which we know is approximately c, because its today-distance from us is 13 billion lightyears. (You show in your post that you understand this.)

You had better try it. Put z = 1.4 into the Morgan, and see for yourself what the standard cosmo model tells you. No verbal stuff can substitute for this.

 

[yogi]

Marcus - Morgan's calculator - good stuff. I am going to make a plot for various parameters and get a visual of how the universe changes.

What I was trying to convey in my post re the 26 billion lightyear distance was based on this: www.atlasoftheuniverse.com/redshift.html

Regards

Yogi

 

[marcus]

Marcus - Morgan's calculator - good stuff. I am going to make a plot for various parameters and get a visual of how the universe changes.
...

Thanks for getting back to me! Glad you checked it out and find it useful.

 

[Wallace]

Be careful not to confuse proper distance with light travel time. Proper distance today means the actual distance you would measure if you could freeze expansion today.

The concept of universally 'freezing expansion today' across a cosmological scale in an unambiguos way violates the fundamental ideas around simultaneity inherent in relativity. You can't talk about 'now' in a universal sense, so when you talk about freezing the expansion 'today' and measuring a distance this is completely aribtrary and depends on the (almost) complete freedom you have to define the 3D surface of constant co-ordinate time you are referring to.

Calling the proper distance as defined in the FRW co-ordinate system the 'actual' distance is a very dangerous thing to do. Much better to understand how arbitrary this is, even if it is clearly a very usefull concept.

For an example discussion, see http://arxiv1.library.cornell.edu/abs/0911.3536" recent pre-print which looks at different ways of describing redshift and recession velocities. I don't neccessarily agree with all the interpretations in that article (I think it overplays its hand a little) but it demonstrates the folly in attaching physical meaning to one treasured co-ordinate system, requiring one to do some mental gymnastics to explain the odd physical intrepretations that it may require.