Having just read Janna Levin's
excellent book "*How the Universe got its spots*", I'm still pondering
her statement that the universe probably appears to be infinite, while it is
most likely to be quite compact. "Quite compact" she admits, may mean
that it is possibly larger than what we can observe, but on the other side of
that horizon, it may just repeat itself endlessly, without actually being
infinite. *Huh?*

OK, I don't quite understand all that
she wrote about the topology that makes such a scenario possible. What I do
understand is that there should be a limit to the size of the universe -
infinite things are not really describable by math, science or in words. If the
universe is now infinite, it must have started out infinitely large at the Big
Bang. *Huh? Again!*

In principle, something that is
finite can never become infinite in size through growing bigger, because then
it must have a size and a thing with size cannot be infinite in size, not so? A finite universe is the only one that makes sense.

Fortunately, the best data that we
have suggest that the cosmos may be just on the closed side of flat. Closed
means it is compact, however big that "compact" may be. It also means
that it can be finite without an edge, because it can fold around on itself,
much like Earth's surface has no edge because it is folded into a sphere. So
how big must such a 'spherical cosmos' be? Here's how big:^{[1]}

This picture suppresses one spatial dimension, so that the universe is portrayed as a two-dimensional surface that is curved into some fictitious hyperspace, hence forming a hypersphere. We have no access to the other dimension (the inside) of the hypersphere. Our observable
cosmos is pictured as the small yellow circle on the surface of the hypersphere, around 28 Giga lightyears (Gly) in diameter, with us in the center of course. The observable 'horizon' appears to be 14 Gy from us in light travel time. Actually, it was about a 300 times smaller (~0.045 Gly radius) when the light that we now observe left the horizon. Due to the rapid early expansion, the light took 14 Gy to reach us.

During the 14 Gy that the light was in transit towards us, that region expanded ~1000-fold, from 0.045Gly to around 45 Gly radius today (the white circle, diameter 90 Gly). We will never see the horizon as it "looks" today, because light will take 45 Gy to reach us! This "observable universe" can however not
be the total cosmos - observations of the visible part point to more of the same on the other side of that horizon.

Measurements of the overall
curvature of space (terribly difficult due to the slight curvature) indicate
that a closed universe must be at least 800 GLy in circumference, almost 10 times the present diameter of the observable universe.^{[2]} We use circumference here and not diameter, because we are talking of something similar to the circumference of the Earth. The previous two regions (circles) are characterized by their diameters, because they are situated on the surface of the incredibly large expanding "ball" of hyperspace. So large that on the scale of our human experience, the hypersphere is pretty much "infinite" in circumference.

In the end, it appears as if the
cosmos is so big that we don't need to care about its size. Also, the cosmos probably
doesn't care much about us either – we are just too insignificant in comparison. We
should rather care more about the three-dimensional oblate spheroid that we call home, Earth, Gaia, or
whatever. At least we know what size it is and it is surely not big enough to
ignore our wrongdoings…

Jorrie

[1] Background artwork is the Cosmic Microwave Background as measured by WMAP. My circles are not quite drawn to scale.

[2] From latest WMAP data by NASA (5-year). I have used rounded values, just to illustrate the points. The 800 Gly minimum circumference comes from the maximum value of the curvature parameter today, **Ω**_{k}** ≤ 0.13**. Then **circumference today ≥ Observable universe diameter today x Π / **√**0.13 ≥ 800** Gly.

1## Re: How BIG is the Cosmos?