# Hubble distance

1. May 21, 2005

### marlon

You know, there are many things in astrophysics, that i do not understand :rofl:

For example, this thing of the Hubble distance. At distances that exceed the Hubble distance the universe is expanding with velocities that are bigger then the speed of light. Suppose that in this region a star emits light, then we would never be able to see that light because this star moves away from us with a velocity that is bigger then the velocity with which the EM-radiation is propagating towards us. But i heard this statement is wrong because as time passes by this Hubble distance gets bigger and bigger. So at some time, the Hubble distance will be bigger then the distance between us and the star and we would indeed be able to see the cosmological redshifted emitted light. Is this correct, SpaceTiger ? How was this discovered in General relativity ?

regards
marlon

2. May 21, 2005

### dextercioby

And if we did see that radiation,what would make us think it's a purely (general) relativistic effect,and not a quantum one,similar in a way to the Hawking radiation...?

Smart question,Marlon. Mine is not bad,either.

Daniel.

3. May 21, 2005

### marlon

Ha, i think we are gonna have to wait awhile because SpaceTiger is very busy writing a post in the "A conceptual problem regarding work" thread...mmm

marlon

ps dexter, is it my imagination or do we indeed get along better since i started doing physics in Leuven ? :)

4. May 21, 2005

### dextercioby

We've never had an argument,remember (i asked Greg to delete the posts,but keep the postcount,so you wouldn't find out ) ?

We've always gotten along just fine...

Daniel.

5. May 21, 2005

### hellfire

The Hubble sphere (with radius = c / H) is not an horizon. In case of a de-Sitter expansion (exponential expansion due to an empty universe but with a cosmological constant), the Hubble parameter is constant through time and the event horizon (limit of objects whose light will never reach us in future) is actually located at the Hubble sphere. Otherwise, for an universe with matter content the event horizon, if it exists, is always greater than the Hubble sphere. Objects beyond the Hubble sphere but inside the event horizon emit photons towards us which are overtaken by the recession of the Hubble sphere (the Hubble parameter decreases with time in an universe with matter content). Photons emitted by objects beyond the event horizon will be never overtaken by the Hubble sphere and will never reach us. May be this paper helps: http://arxiv.org/astro-ph/0310808 [Broken].

Last edited by a moderator: May 2, 2017
6. May 21, 2005

### SpaceTiger

Staff Emeritus
Horizons are calculated by examining the motion of a light ray in comoving coordinates. Why comoving? Because we want to know how the light moves relative the galaxies, which are expanding. The Friedmann-Robertson Walker metric for a flat, homogeneous and isotropic universe is

$$ds^2=dt^2-a(t)^2dr^2-a(t)^2r^2d\psi^2$$

where I've set c=1. If we're following a photon moving radially, we have ds=0 and $$d\psi=0$$, so it simplifies to:

$$dt=adr$$

So if we want to see how far it goes from t=0 (the big bang) to some later time, we get

$$r=\int_0^{t_0} \frac{dt}{a(t)}$$

This is the particle horizon. Likewise, we can define an event horizon as the comoving distance it travels from t=t0 to infinity:

$$r=\int_{t_0}^{\infty} \frac{dt}{a(t)}$$

The fate of the photon depends on the model of the universe that you're using. The current universe is a bit complicated, but we can examine the limiting cases. Until recently, the universe was well described by a flat, matter-dominated model. This gives a scale factor dependence of

$$a(t)=a_0t^{2/3}$$

Putting this into the equation for the particle horizon, we get

$$r_p \propto t^{1/3}$$

That is, people observing the universe at later times can see more of it. Notice also that the event horizon diverges, meaning that a light ray emitted from the earth will eventually explore the whole universe.

This is not the universe that we live in, however. We currently think that the late-time expansion of the universe will be dominated by a "cosmological constant", a field with constant energy density that pervades the universe. By the Friedmann equation in a flat universe:

$$H^2=\frac{8\pi G\rho}{3}$$

a constant energy/mass density will mean a constant hubble constant. What does that mean for the scale factor?

$$H=\frac{\dot{a}}{a}$$

$$a=a_0e^{Ht}$$

This is exponential expansion. Finally, we can plug this into the equation for the event horizon and get:

$$r_e=\frac{1}{a_0H}e^{-Ht_0}$$

A finite value! This means that, with our current understanding of the universe, we don't think that we, or anyone else, will ever be able to see or communicate with the whole thing. I wouldn't put a lot of faith in our current models, though, so think of this instead as one possibility.

Note 1: Hellfire is right that none of the things we're concerned about here are called the "Hubble horizon", but I just assumed you meant the particle and event horizons.

Note 2: Please feel free to ask me to explain any of this further, I was a bit liberal with the math and terminology this time around.

Last edited: May 21, 2005
7. May 21, 2005

### Nereid

Staff Emeritus
Daniel and marlon: have you taken the time to read through Ned Wright's Cosmology tutorial? It contains links to his full set of lecture notes for two university courses on cosmology ... if you do take a gander, would you mind letting us know if you find the material useful? interesting??

8. May 22, 2005

### marlon

Thanks SpaceTiger for the text and thanks Nereid for the link...Give me some time to check it out

regards

marlon

9. May 23, 2005

### Haelfix

Hellfire is 100% correct.

We can in principle (with an open-expanding universe) see objects that are receding at faster than light, this has caused a lot of confusion and is often badly explained in text books.

To wit, our particle horizons is LARGER than our event horizons. So while we will never see an actual event in a galaxy that has passed our event horizon, we can still see the galaxy as it was from long ago, from a time when it was within our event horizon.

The other related confusion is how people note Inflation is superluminal expansion, whereas standard cosmology is not. This is misleading, and may or may not be correct. All objects that satisfy Hubbles law have superluminal expansion if they are sufficiently distant from an observer. The only difference is in inflation the Hubble constant is much larger than after it is over. Really to fully justify calling Inflation 'pure superluminal expansion' you would want all distances, down to the Planck scale to be receding faster than light, or in other words some huge value of Hubbles constant (and it is probably never that large)

10. Jun 4, 2005

### Andrew Mason

I share a similar sense of bewilderment about the theories of astrophysics. I have never really understood why a period of superluminal expansion is thought to be needed to explain the post-big bang universe.

I don't think it has ever been established that the universe exists at distances greater than C/H. Absent some superluminal 'expansion', C/H represents the maximum radius of the universe.

As you point out, H is not really a constant. H represents inverse time... so as time passes, H decreases. Also H is frame dependent. I think C/H will always exceed the width of the universe in every frame of reference (as H is measured in that frame).

AM

11. Jun 4, 2005

### yogi

AM - I would agree - I like to envision the Hubble Sphere as a closed two dimensional universe - every observer at any point on the surface of this expanding bubble can see all other observers - the observers are not aware of the curvature, so all other points appear to be moving away in a plane tangent to the surface of the sphere at the observers location (a two dimensional radial divergence). In other words, all observers share the same space and each can see light that is emitted from any point on said surface if they wait long enough, but each views the same universe from his own perspective.

Open Universes lead to many questions that don't get easily answered - similarly, inflation also creates problems which might be easer solved by assuming an exponental spaciotemporal scale - e.g., expansion may be driven by an exponential function as are many other naturally occuring process. One of the nice results of these musings is that there no longer has to be a beginning in the spatial or temporal sense.

12. Jun 4, 2005

### pervect

Staff Emeritus
13. Jun 6, 2005

### Andrew Mason

The horizon problem seems to be the result of a disparity between the age of the universe and the size of the universe. But neither of these are values have been reliably established. Until they are, it seems rather premature to get worked up about 'contradictions' and the need to invent fancy explanations for them.

AM

14. Jun 6, 2005

### pervect

Staff Emeritus
The horizon problem is related to the issue that the big bang is not a point, but has a causal structure. The causal structure is such that we wouldn't expect the microwave background radiation to be isotropic without some mechanism such as inflation.

15. Jun 6, 2005

### Andrew Mason

Why?
If the big bang produced a uniform isotropic explosion of whatever it was that exploded out of it (and which later formed into quarks, electrons, nuclueons atoms photons etc, lets call it big bang stuff) presumably the big bang stuff would all behave in the same way in all directions.

The stuff on the outer edge of the expanding universe would be travelling at something very close to the speed of light (very large gamma) so the radiation it emitted would be doppler shifted into the microwave range. The isotropic nature of that radiation is simply the result of the stuff on the outer edge of the universe having been created at the same time and having the same speed.

In other words, and I may be missing something, the causal connection seems to me to be with the common origin of the stuff on the outer edge of the exploding universe.

AM

16. Jun 6, 2005

### pervect

Staff Emeritus
The common idea of the big bang is a more-or-less single cause that occurs at a single point that caused the universe.

Not only is this the common idea, it's the idea that the isotropy of the microwave background radiation supports. The temperature of the universe is nearly the same in all directions, suggestion that all of the microwave background radiation came from some sort of single cause, this cause set the temperature that we observe.

There is only one small problem with this idea, and that is that the solutions of GR wihtout inflation say that the events that we see on the "left side" of the universe do not and never did have any common history with the events we see on the "right side" of the universe.

But nonetheless we see that these events have almost exactly the same temperature.

Inflation solves this dilema, by providing a means whereby past history can affect both events.

I'd suggest going back and reading the links I quoted - not only can the authors write in more depth than I can in a post, they can include diagrams.

17. Jun 6, 2005

### Garth

The horizon problem is caused by the deceleration of the universe's expansion - an inevitable feature in Friedmann cosmology of a non-empty universe. However we do not live in a Friedmann universe, apparently the universe is accelerating, and this would reverse the horizon problem - everything could be in causal contact with the earliest space-like surface of the observable universe. However recent (distant SN Ia)acceleration is switched on and off and as a result cannot itself resolve the horizon problem. That is why the enormous acceleration of the inflation epoch is required.

However if the universe is not decelerating in the first place e.g. in the “Freely Coasting” model then the horizon problem does not exist in the first place, neither do the smoothness and density problems, and inflation is not required. Occam's razor anybody?

Garth

18. Jun 6, 2005

### DrChinese

I believe that your explanation inevitably leads to the prediction of shock waves in the CMBR which aren't seen by WMAP. The accelerating expansion models don't suffer from this feature.

19. Jun 6, 2005

### Andrew Mason

Do you mean "common history" or "causal interaction"? The events on the far left side of the universe may have had no interaction with those on the far right side. But they may well have had a common history.

The light cones of these events may not intersect at any time after the big bang. But that does not mean they lack a common origin and history.

I guess one has to see it as a dilemma first. It seems a bit like pulling a rabbit out of a hat. I don't see any evidence for it.

Hyperphysics has a pretty good explanation of some of these issues.
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/inflat.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cosmo.html#c5
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/wmap.html#c1

AM

20. Jun 6, 2005

### pervect

Staff Emeritus
Let me see if I can clear something up - if we look at Ned Wright's conformal diagram at the end of

http://www.astro.ucla.edu/~wright/cosmo_03.htm

are you saying that conformal time extends backwards indefinitely in the freely coasting model, instead of stopping at the bottom of the page, so that the yellow triangles do overlap (?).