Cosmology: Expansion & Its Impact on Us - Jens

[jensel]

Hi,

I have one question about the expansion of the universe.
Say, that there is a part which is that far away that we can't see it
any more more because the speed of light is succeded.
Wouldn't this mean that those part of the universe has no more influence on
us at all?
In ohther words: Where do I see this say cut-off in the equations?Jens

 

[zhermes]

You're exactly right.
The parts of the universe which are receding from us faster than the speed of light are called 'causally disconnected' because they will never have any influence on us.

In general relativity (i.e. 'the equations'), these regions are outside of our 'light-cone' (which describes the region that is causally connected), and thus never effect us.

 

[George Jones]

You're exactly right.
The parts of the universe which are receding from us faster than the speed of light are called 'causally disconnected' because they will never have any influence on us.

In general relativity (i.e. 'the equations'), these regions are outside of our 'light-cone' (which describes the region that is causally connected), and thus never effect us.

This is false. Regions of the universe receding from us with speeds greater than the speed of light are not necessarily outside of our past lightcone.

As I said above this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c. It might seem that moving to a recession speed of c represents a transition from subset 1) to subset 2), but this isn't the case.

Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.

In more detail:

I know this is very counter-intuitive, but I really did mean what I wrote in posts #52 and #55.


Thanks for pushing me for further explanation, as this has forced me to think more conceptually about what happens.

This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:

O                                B        A        C
*                                *        *        *


*                    *     *     *
O                    B     A     C

The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, $t_e$. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, $t$. Notice that space has "expanded" between times $t_e$ and $t$.

Suppose that at time $t_e$: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time $t$, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because A's recession speed at time $t_e$ is greater than c, the pulse fired towards us has actually moved away from us between times $t_e$ and $t$.

Now, suppose that the distance from us to galaxy B at time $t$ is the same as the distance to galaxy C at time $t_e$. Even though the distances are the same, the recession speed of B at time $t$ is less than than the recession speed of C at time $t_e$ because:

1) recession speed equals the Hubble constant multiplied by distance;

2) the value of the Hubble constant decreases between times $t_e$ and $t$.

Since A's recession speed at time $t_e$ is greater than c, and galaxy C is farther than A, galaxy C's recession speed at time $t_e$ also is greater than c. If, however, the Hubble constant decreases enough between times $t_e$ and $t$, then B's recession speed at time $t$ can be less than c. If this is the case, then at time $t$ (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times $t_e$ and $t$.

If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time $t_e$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time $t$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.

Probably some of my explanation is unclear. If so, please ask more questions.

 

[zhermes]

This is false. Regions of the universe receding from us with speeds greater than the speed of light are not necessarily outside of our past lightcone.

Of course they're not outside of our past light-cone. While I didn't specify, I was referring to future light-cone (as appropriate to the OP's question).

And while I somewhat see what you're saying @George, If something is outside the cosmic event horizon, then it will always be outside, by definition. And as distant regions of the universe are receding faster than the event horizon, things are only exiting our future light-cones. No?

 

[bapowell]

And while I somewhat see what you're saying @George, If something is outside the cosmic event horizon, then it will always be outside, by definition. And as distant regions of the universe are receding faster than the event horizon, things are only exiting our future light-cones. No?

Right, but George's argument refers to the case $\dot{H} < 0$. In this case, the Hubble radius is not equivalent to the cosmic event horizon (which is larger, if it exists at all -- I say this because the OP refers perfectly well to standard non-accelerated cosmologies where there is no event horizon), and so objects that achieve recession velocities greater than c are not outside the event horizon. The coincidence of Hubble scale and event horizon scale occurs only for de Sitter expansion, H = const.

 

[zhermes]

Gotcha; thanks.

 

[jensel]

Thanks for the replies! Would you agree: If there is a cosmological model where the current state of our position is outside the infulence of parts moving > c, outside of any influence, wouldn't this influence the model itself? We are talking about Black "Objects" where normally no information is exchangable. Photons are not able to get outside the event horizon... Gravitons are? Gravitons who have to excist because we make the ART in the lower limit linear? Gravitons which have by definition mass, they are able to "fly around", no matter if there is an event horizon? And this in this in theory which is by definition highly nonlinear?

Thanks,
Jens

 

[jensel]

Well, normally I should delete my last posting because it is not correct to compare a black hole with the universe. As well as I understand there is a big difference between both, let's say type of event horizon. A black hole is gravitating because no mass dissappears within the event horizon, right? Now, if we analyse the situation for the cosmos for gravitation/gravitons then there is no more link to parts being not in the light cone. For me this clearly shows that the effective mass will shrink. This means naturally an influence on the Friedman equations. From the derivation I would say there is no cut-off in the influence of matter being outside the possible influence. If we accept this cut-off I probably could easily show that there is an acceleration in a(t). This naturally wouldn't explain if we have really something like a(t) ~ exp(t) but at least that $\ddot{a}>0$.
Do I think right or is this completely nonsense?

 

[jensel]

PS: If
$\dot{a} \sim a$ we see immediately that it is going
$a \sim exp(t)$
which I find natural (without having this calculated, sorr, I shouldn't be that lazy) if we have a linear loss of effective mass.

 

[Tanelorn]

You're exactly right.
The parts of the universe which are receding from us faster than the speed of light are called 'causally disconnected' because they will never have any influence on us.

In general relativity (i.e. 'the equations'), these regions are outside of our 'light-cone' (which describes the region that is causally connected), and thus never effect us.

Well wouldn't a galaxy from just beyond our observable universe still be causually connected to one just inside our observable universe, which would be causually connected to one closer to us and so on and so on? So in fact the regions beyond our observable universe still play an important part in the behaviour of our observable universe?

 

[DaveC426913]

Well wouldn't a galaxy from just beyond our observable universe still be causually connected to one just inside our observable universe, which would be causually connected to one closer to us and so on and so on? So in fact the regions beyond our observable universe still play an important part in the behaviour of our observable universe?

Nope. Galaxy 2 may be able to affect Galaxy 1, but not in time for it to have any effect us in Galaxy 0.

 

[Tanelorn]

Dave, yes, I see that there isn't enough time for it to effect us here, but could we not observe the effects of mass beyond the observable universe on mass just inside our observable universe? Dark Flow was a name I remember related to this but I see some now think that this is flawed.

Does not the behaviour of mass at the edge of our observable universe tell us that there is mass beyond it?



Well in an attempt to answer myself I see that the observable universe is:

"The comoving distance from Earth to the edge of the observable universe is about 14 billion parsecs (46 billion, or 4.6 × 1010, light years) in any direction. The observable universe is thus a sphere with a diameter of about 29 billion parsecs[15] (93 billion, or 9.3 × 1010, light years)[16]. Assuming that space is roughly flat, this size corresponds to a comoving volume of about 3.5 × 1080 cubic meters. This is equivalent to a volume of about 410 nonillion cubic light-years (4.1 × 1032 cubic light years)."

Of course we can only observe galaxies out to z=8.6 so that probably makes my question meaningless.

I am not sure how far away z=8.6 is, but compared to z=1030 for the comoving light, we only see a very small fraction of the matter in the observable universe.

 

[Tanelorn]

Using the cosmos calculator to better understand the expansion distances in my previous message:

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html


For the CMBR:

Matter density = 0.272
Cosmological constant = 0.728
Hubble constant = 70.4
Redshift = 1091


age of universe now = 13.75 billion years
distance of object now = 45.73 billion light years
speed away from us now = 3.29c

age of universe then = 0 billion years
distance of object then = 40 million light years
speed away from us then = 56.75c !
hubble constant then = 1324924



For the most distant galaxy with z=8.6:

Matter density = 0.272
Cosmological constant = 0.728
Hubble constant = 70.4
Redshift = 8.6


age of universe now = 13.75 billion years
distance of object now = 30.56 billion light years
speed away from us now = 2.2c

age of universe then = 0.59 billion years
distance of object then = 3.18 billion light years
speed away from us then = 3.56c
hubble constant then = 1094



So if the above is correct, relative to us, this galaxy is currently not that far away from the current position of the CMBR (well 15 Billion light years), which by definition, the CMBR is the edge of the observable universe.


Also interesting that the distance of this galaxy from us then is just 30,000 times the current diameter of our galaxy.
A distance of just 30,000 times the diameter of our galaxy is also the distance limit of our Hubble deep field survey, because we can only see the universe as it was then.

The most current estimates guess that there are 100 to 200 billion galaxies in the Universe, each of which has hundreds of billions of stars. Is this consistant with the volume available in distance of 30,000 times the diameter of our galaxy? By universe, do they mean one the size of the CMBR observable universe? I just did a very quick calculation and I get an even higher number; a maximum possible number of galaxies = 10^13, however back then it would have been a very tight fit!

http://www.universetoday.com/30305/how-many-galaxies-in-the-universe/