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The size of our observable universe must have grown over time in the early universe. Conversely with the accelerated expansion, I have heard that eventually our observable universe will shrink down to our local group of gravitationally bound galaxies. So then the observable universe must go through a maximum at some point in time. When is that and what is that maximum size?

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I am sorry I should have been more precise. I think I really meant when is the time when we can observe the maximum mass? I suspected that it might be 'now'. With the current 'standard model' in cosmology - lambda CDM - there must be an estimate in terms of lambda and H?? –  Steve C Feb 17 '11 at 3:58
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4 Answers

There's a lot of confusion here, which is not surprising given that a few things are going on.

The physical distances in the universe e.g. between galaxies - measured in meters, miles, parsecs, or other favorite units of yours - will continue to increase since the universe will continue to expand. In fact, as the universe becomes completely dark energy dominated (soon - in some dozen billion years), the physical distances will increase exponentially in time, $d_P\propto e^{Ht}$, where $H$ is the Hubble parameter which is now decreasing (it's equal to 71 km/s/Mpc today, and going down), but will stabilize to a constant when DE takes over. So $H$ in that exponent will become constant, the distance will increase purely exponentially.

On the other hand, the radius of the observable part of the universe - the "horizon distance" discussed in some other posts here - is increasing slower, and will actually come to a halt. This becomes clear once you recall that the horizon distance is proportional to $1/H(t)$. The Hubble parameter $H(t)$ will, recall, become essentially constant 'soon', and so will the horizon distance.

So all of your favorite faraway galaxies are moving away from you (almost) exponentially with time, while the radius of the observable universe becomes (almost) constant. What gives? The galaxies are leaving our observable universe (because of dark energy, remember)! Those far away first, those closer to us later. This is the origin of the statement that only objects gravitationally bound to us - our Solar System, Milky Way Galaxy, and the Local Group - will remain observable a few tens of billion years in the future.

The original question was then something to the effect of 'when can you see the most galaxies in the universe'? In principle, this question should be easy to answer (the largest-number-of-galaxies moment has already happened I believe). But in practice the exact answer might be hard to calculate, since galaxies also have an annoying habit of being created and destroyed (e.g. by their collisions etc), not just sitting still. I have not done a back-of-envelope calculation to try to estimate this, but one could.

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Nice answer. My only quibble would be that your analysis is dependent on the assumption that dark energy behaves in a certain way: that the cosmological "constant" really is constant. We actually don't really have any data on whether that's the case. For some equations of state you can get scenarios like a "big rip." –  Ben Crowell Aug 5 '11 at 1:30
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A related post from arXiv blog. Cosmos At Least 250x Bigger Than Visible Universe, Say Cosmologists.

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The observable universe is currently increasing in size at the rate of one light year per year. The universe itself is currently expanding at around 71 km/sec/Mps, so we can still receive incoming light. Even though we are in cosmological constant dominated cosmology and accelerated expansion, the observable universe will not hit a maximum until space is expanding at a rate greater than c. The definition of observable universe is what we can see (or record) because of light that has had time to reach us since the big bang. The size is about 47 billion light years or 14 billion parsecs currently.The future visibility limit is at a co-moving distance of about 19 billion parsecs. There does seem to be some variation in the definitions though. The Hubble volume is the volume out to the distance where objects recede from us at greater than the speed of light. Because of the accelerating expansion, the Hubble volume is decreasing.

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I think I’ll delete my answer and let you deal with this, I have no time to fine tune things at the moment and your answer is basically identical to mine, except where it is better... –  user566 Feb 17 '11 at 3:53
@moshe-lol. No offense--I didn't mean to horn in, and when I read your answer didn't realise at first you were describing the Hubble volume. –  Gordon Feb 17 '11 at 3:57
Not a problem, it really doesn’t matter as long as the right answer is out there. You just have to correct the references to my answer which is no longer visible. –  user566 Feb 17 '11 at 4:13
The observable universe is not currently increasing in size at the rate of one light year per year. Here is a nice popularization that deals with this and some other popular misconceptions: mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf If the rate of expansion had always been 1 ly/yr, then the radius of the observable universe would have to be 14 billion ly, but it isn't -- it's 46. –  Ben Crowell Aug 5 '11 at 1:25
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In 10 billion years we will be able to see galaxies in the local group by optical means. If one were to look with IR it would be possible to see galaxies which have receded further out and are moving out at a faster rate. If one used millimeter wavelength it is possible then to see very distant galaxies that we can now see in the optical or IR. The CMB will not be visible in the microwave, but radio wave band. Every bit of the universe we see today is in principle observable in the future. Of course as the universe expands and accelerates further it will require radio astronomy to detect any galaxy beyond what then will be the merged Andromeway galaxy and the CMB would only be observable as very long wavelength radio waves. As time marches on the photons from anything not gravitationally tied to our galaxy will become indefinitely redshifted. So all of the universe is still available for observation, just ever more redshifted

Also in 100 billion years the galaxy will dimly glow with red dwarf stars. The universe is generally getting darker and colder.

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"Every bit of the universe we see today is in principle observable in the future." This is incorrect, for the reasons explained by Dragan Huterer. –  Ben Crowell Aug 5 '11 at 1:29
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