FYI, it is generally assumed that the universe is properly infinite; any finiteness of the universe is determined only by the horizon we can see. Which is 13.8 Gly proper distance, or ~45Gly of visible universe (which includes matter that has since passed beyond our horizon).

The expansion of space-time should not be understood as a mechanistic motion of bodies. It is the consequence of setting up boundary conditions, and solving for the field equations over time:

https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metricAs it turns out, if you fill space with a constant density of matter, it is the nature of space that it expands over time. There is a single parameter corresponding to the density of matter, and its consequential expansion rate and history (the curvature of spacetime). A parameter which, so far as we can tell, is very nearly neutral (the curvature is flat), so that the universe is expanding precisely fast enough to avoid falling back in on itself (a "big crunch" would be spiritually satisfying, but is not supported by any data), which also gives the longest possible lifetime of the universe before objects fall out of each others' horizons ("big rip", give or take if the expansion accelerates or not, which currently it looks like it is tending to accelerate).

So, considering where we are now, if we wind the clock back, the universe remains infinite in extents, though there is much more matter within a given horizon.

Distance itself is not changing over time. Size scales are fixed. Particles and objects are the same sizes they've always been (well, as far as we can tell). The distances between reference points are what's changing.

At least, we have no particular reason to doubt that objects have the same dimensions as usual -- that, for example, in the early history of the universe, the highest stable density of an object is still given by the same formula and constants as we observe today. So, for example, not so much the Chandrasekhar limit which has to do with white dwarfs (which weren't seen until much later in the history of the universe), but, the Schwarzschild radius should be the same. That is, the radius within which matter collapses to form black holes -- primordial black holes are predicted to have been produced in the early universe. Or the relations of energy to wavelength (Planck's constant), stuff like that.

If we continue winding the clock back, we expect ever-higher energy levels, with ever-higher mass densities, eventually culminating in some exotic states of matter in the earliest zeptoseconds of the universe.

At time zero, the universe is still infinite, but its size is zero. All particles are within each others' horizons (if particles are even a meaningful concept at this scale), density is infinite, energy is infinite... Suffice it to say: it isn't meaningful to think about physics at zero time -- you're looking at a point where the value is

*undefined*. It's only meaningful to consider the limit

*up to*, approaching, that point.

Some have toyed with the idea of complex time, as an analytical tool. Where a real-ranged function gives an infinite or undefined result, we can look

*beside* the point, at complex values (assuming a complex analytical extension to the function exists, and is reasonable), and try to go around it instead. We can still get reasonable answers out of this method, even if we've performed the analysis through completely unreasonable means (what the

*fuck* is "complex time" supposed to mean? Nothing, so don't worry about it!), and as long as we understand that those means may or may not be applicable to all cases.

I forget if anything significant came of imaginary time; this,

https://en.wikipedia.org/wiki/Imaginary_timelooks like it's a casual thing, as much a quirk of how one chooses to write the equations, as it is useful to solving them, so not remarkable in and of itself. ("Complex numbers" are another one of those things in mathematics that's regrettably named. The domain is really not much more complicated than the reals -- which I say are named even worse, there's nothing "real" about them -- and indeed the complex numbers are more general, so you don't have stupid special cases like not being able to say sqrt(-1), or not being able to solve x^2 + 2x + 2 = 0, or not needing half a dozen trig functions when only one (exp) will do, or...)

Tim