New model predicts the size of the cosmos
Speaking of assumptions, here's a new paper that blows the standard assumptions about the curvature of the universe out of the water.
Almost all work on predicting the actual physical size of the cosmos is based on an assumption about the curvature of the universe--whether it is closed (curvature < 0), flat (curvature = 0), or open (curvature > 0 ( Read more... )
Almost all work on predicting the actual physical size of the cosmos is based on an assumption about the curvature of the universe--whether it is closed (curvature < 0), flat (curvature = 0), or open (curvature > 0 ( Read more... )
This compares to the maximum diameter the universe would be if the universe were not expanding: 28 billion light years in diameter, i.e. twice the time (14 billion years) since the Big Bang.
22.5 trillion is a little over 800 times 28 billion. Is the 800x difference due entirely to expanding space-time? How fast is the matter in the universe traveling when we factor out the contribution of expanding space-time?
I still have no idea what is meant by flatness or curvature of the universe. I've seen the graphics illustrating positive curved space (a sphere), flat space (a piece of paper), and negative curved space (a folded piece of paper). But I don't understand how that relates to how matter is laid out in the universe. Galaxies appear to be laid out in three-dimensional space. So how that 3D display of galaxies can be re-conceptualized into a lay out more akin to a piece of paper, I don't understand.
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The typical illustrations you'll see for curvature all involve the projection of three-dimensional space onto two dimensional surfaces. That's convenient because everyone can easily imagine it, but it breaks down when you start getting into the details.
Um. Here, believe it or not Wikipedia has a pretty good entry on this:
http://en.wikipedia.org/wiki/Shape_of_the_Universe
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That's the maximum visible diameter of the universe if the universe isn't expanding, not the maximum physical diameter. In the case where the universe isn't expanding, it can be infinite if you want: that's just how big it is, set by some initial conditions we don't understand. So the comparison to make is the 28 billion light years to the 90 billion light years.
And yes, the difference there is due to the expanding universe. It's sort of like...say the only way you know where I am is I throw a ball at you and you catch it. I can only throw a ball 5 feet. However, I can throw the ball at you and then run away in the time it takes for the ball to get to you. You know I'm there, but I can now be more than 5 feet away from you due to that movement. If you have a way to know how fast I was running when I threw the ball at you, you can know where I am beyond the 5 feet I can communicate with you. The objects we see in the universe are moving away from us; we know how fast due to the redshift of the light that reaches us, so we can say that these objects are now further away than the 14 billion light-years they'd be if they weren't moving. That's roughly why the visible universe is bigger in the expanding universe case. (There's an added effect in the real world, where that 5 feet that I was able to throw the ball is actually changing while the ball is in midair, but I can't think of a way to work that into the analogy...)
How fast is the matter in the universe traveling when we factor out the contribution of expanding space-time?
It's basically not moving at all. I mean, individual pieces of matter are moving as they are pulled by the gravity of nearby objects (the Earth is rotating around the sun, the sun is moving around the center of the Milky Way, the Milky Way's moving towards Andromeda) but if you compare the "movement" of the Earth relative to some object billions of light-years away, all of the relative motion is caused by the expansion of spacetime. The matter isn't moving relative to the spacetime at all (except for gravitational motions); it's just the spacetime between distant objects expanding.
And yeah, galaxies are laid out in three-dimensional space. The pieces of paper are two-dimensional analogies, but you can't really picture the three-dimensional version because it would require a fourth spatial dimension to curve into; we don't have four spatial dimensions so we can't picture it. There are two ways to think about curvature that...well, "make sense" probably isn't the right phrase; are easier to understand, maybe?
1. The triangles way. You're in a spaceship. You travel to some hugely distant galaxy. You get there, make a sharp right turn at exactly 90 degrees, and travel to another galaxy. You then turn to head back to the Milky Way, measuring the angle you turn, and when you get back to the Milky Way you measure the angle from the direction you just came to the first galaxy you visited. In a flat universe, the Pythagorean Theorem works; the three angles you measure add up to 180 degrees and you can do the a^2+b^2=c^2 thing with the length of the sides. In a positively curved universe, the three angles add up to more than 180 degrees, and in a negatively curved universe, they add up to less than 180 degrees. It's just like doing triangles on the surface of a sphere or the surface of a saddle.
2. The density way. In a closed universe (positive curvature) with no dark energy, there's lots of matter around to exert gravitational influences on each other. Eventually that attraction overcomes the expansion of the universe and everything comes together in a big crunch. In an open universe with no dark energy, there's not much matter, so the universe expands forever. The limiting case (flat universe) expands forever, but at an always-decreasing rate. It's very likely that we *do* have dark energy, so the fate of the universe doesn't match any more, but that doesn't change the way people define flat, open, and closed from the current density.
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