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Currently, even the nearest stars are lightyears away, and impossible to reach in our lifetimes. If space is always expanding, and was once infinitely smaller, then at what point in the past was space so much smaller that the average distance between stars was less than light days? Was there ever such a time?

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    $\begingroup$ Hi Ben Warner: Welcome to Phys.SE. Did you try to do a back-of-an-envelope-calculation? $\endgroup$
    – Qmechanic
    Sep 6 at 8:13
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    $\begingroup$ see this astronomy.com/magazine/ask-astro/2006/01/… . We just happen to be around a star at large distance from other stars. " A typical stellar separation at this density works out to 0.008 light-year, or 500 AU — about 12 times the Sun-Pluto distance — between stars." $\endgroup$
    – anna v
    Sep 6 at 8:18
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    $\begingroup$ Sure, it's impossible for humans to travel that far with current technology, but it's not impossible, in principle. However, no matter what technology is used, it takes a lot of energy to travel even 4.5 lightyears in a human lifetime. $\endgroup$
    – PM 2Ring
    Sep 6 at 9:32
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    $\begingroup$ I don't think that just because things were a few light days apart, meant that they could be travelled between in a few days. Space would have expanded while you were travelling between them, so depending on how fast the expansion was, it may have been that it took a photon years to travel between two points that were, when the photon left the first point, only light days away. $\endgroup$ Sep 7 at 3:39
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    $\begingroup$ Depends on the elements you need for the spaceship. The first stars were 100M~250M years after the BB, and the only elements were hydrogen and helium. You need Population I stars, and those are only 1M~100M years old. So if it's 13.8 billion years old, more or less the same size it is now. $\endgroup$
    – Mazura
    Sep 8 at 10:13
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As the universe expands each individual galaxy stays roughly the same size, with stars on orbits of roughly constant diameter, so the stars within any given galaxy were no closer together a long time ago than they are now (at least as far as cosmic expansion effects are concerned).

The distances between galaxy clusters were smaller in the past, and a good way to get a sense of this is to note that the ratio of distance between them now to distance between them a long time ago is equal to the ratio of wavelengths in the light received and emitted. If we receive light from a galaxy and the light arriving has a wavelength twice as large as when it set out, then the universe was half as small when the light set out (that is, distances between galaxy clusters were then on average half what they now are).

To find a time when galaxies were not many lightyears apart you have to go so far back that you arrive at times before the formation of galaxies, so there never was such a time.

[Added remark in answer to a question in the comments concerning galaxy clusters. One galaxy cluster drifts away from another because the initial conditions gave them velocities of this form. This general condition is called the "Hubble flow" and it leads to the cosmic expansion. It is what things would do if they only experienced the average cosmic gravitation, without any local bumps owing to a non-homogeneous matter distribution such as a galaxy. Meanwhile everything attracts stuff near to it and this can lead to bound groups such as solar systems, galaxies and galaxy clusters. This binding is sufficient to turn the relative velocities around so that each bound group does not drift apart, nor does it expand (unless some other process intervenes).]

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    $\begingroup$ Where stars ever closer together before the formation of galaxies though? $\endgroup$ Sep 6 at 19:46
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    $\begingroup$ How does "… each individual galaxy stays roughly the same size but the distances between galaxy clusters were smaller in the past…" work, please? Here, is there a significant difference between individual galaxies and galaxy clusters? $\endgroup$ Sep 7 at 4:12
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    $\begingroup$ @RobbieGoodwin It's my understanding that galaxies stick together because the matter in them is gravitationally bound to itself. Eventually, basically all the matter in the reachable universe will be contained entirely in the Milky Way-Andromeda galaxy (long after they've fused together). $\endgroup$
    – nick012000
    Sep 7 at 6:05
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    $\begingroup$ @RobbieGoodwin "All the matter in the reachable universe", not "all the matter". I.e. the matter in the galaxy will remain reachable because it is gravitationally bound, but everything else will be too far away and receding too fast to reach (assuming the universe doesn't later contract and barring something like an Alcubierre drive). $\endgroup$
    – JBentley
    Sep 7 at 14:27
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    $\begingroup$ The question is about interstellar travel. Not intergalactic travel. So the argument against it shouldn't be that galaxies didn't exist. It'd have to be that stars didn't exist. $\endgroup$ Sep 7 at 19:44
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Although the distance between stars doesn't really change due to the expansion of space over the evolution of the universe, the region of space around our Sun is quite sparse compared to some places in the universe. As such, your desired conditions could exist not in the remote past but today, just in a different location.

Here's an article which says "In the center of the galaxy, stars are only 0.4–0.04 light-years apart". 0.04 light years is less than 15 light days.

And another article I found with some quick googling claims:

But some galaxies pack stars even tighter. M32, one of the Andromeda Galaxy's satellites, has the highest measured stellar density of any nearby galaxy — around 20 million stars per cubic parsec in its core! Not even HST can resolve M32's core into individual stars. A typical stellar separation at this density works out to 0.008 light-year, or 500 AU — about 12 times the Sun-Pluto distance — between stars.

0.008 light years is just shy of 3 light days.

These figures come from "average" or "typical" distances to nearest neighbour in dense regions, implying that there will be some even closer than that. How much closer is possible/plausible, I couldn't really say.

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    $\begingroup$ It is doubtful, however, that such regions of space would support or evolve life as we know it. $\endgroup$
    – eps
    Sep 7 at 1:15
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    $\begingroup$ @eps Would it even allow for stable planetary orbits? $\endgroup$
    – nick012000
    Sep 7 at 6:06
  • $\begingroup$ @nick012000 Yes it would. Unless you down to something more like 15 hours than 15 days, Jupiter stays in orbit. $\endgroup$
    – Joshua
    Sep 7 at 20:29
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    $\begingroup$ @SoftwareEngineer These figures come from the typical separation distances in galactic cores, where there are billions of stars packed (relatively) close together. A supermassive black hole is not a "typical" neighbouring star. $\endgroup$
    – Ben
    Sep 8 at 0:08
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    $\begingroup$ And even 3 light days is a hell of a lot. It's about three times the distance that Voyager 1 traveled so far, putting a question mark behind "in our lifetimes", even when assuming that the next star system would actually harbour a habitable candidate (the chances against which are, well, astronomical...) $\endgroup$
    – DevSolar
    Sep 8 at 8:20

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