#### So where are these parallel universes?

So where are these parallel universes if they exist? Well, it depends on the model, because there are many models and each model proposes a different kind of parallel universes. In some models, for instance in the inflationary universe model (the ultra-fast expansion of the universe in its initial instants), you have a single universe but within this universe you have very large regions which in the past have been subjected to inflation, namely a specific process that greatly extends the size of space, creating a sort of bubbles of space-time, but with specific physical properties. And if the model of what we call chaotic inflation did not occur in the same way in all the places in space and time, it would create many bubbles with different physical properties.

#### """The World of the Nations"", by John Murray"

Flat is just a two-dimensional analogy. What we mean is that the Universe is 'Euclidean', meaning that parallel lines always run parallel, and that the angles of a triangle add up to 180o. Now, the two-dimensional equivalent to that is a plane, an infinite sheet of paper. On the surface of that plane you can draw parallel lines that will never meet. A curved geometry would be a sphere. If you draw parallel lines on a sphere, these lines will meet at a certain point, and if you draw a triangle its angles add up more than 180o. So the surface of the sphere is not flat. It's a finite space but it's not flat, while the surface of a torus is a flat space.

#### The light rays intersect

Now, imagine you’re standing at the point where the light rays intersect. If you turn to one side, you will see the object that reflected the ray. If you turn to your other side, you will see the same object but from a different angle. So if the reflective object was a distant planet, you would see the same planet twice. Scientists have already begun to look for this hall of mirrors effect in the dim glow left over from the Big Bang. It would provide evidence of not just the size but also the shape of the cosmos.

#### Silicon Valley: The invisible universe’s geometry

Current measurements aren’t accurate enough for us to know whether the universe’s flat geometry is represented by a piece of paper, a cylinder, torus, or any other shape that permits the parallel passage of two beams of light. An infinite universe could have a geometry that is totally flat like a piece of paper. Such a universe would go on forever and include every possibility — including endless versions of ourselves. On the other hand, a donut-shaped universe would have to be finite, as it's closed. But for now we still don't know the shape of the universe, and therefore nor can we know its size No. We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.

#### Voyagers in the jungle of the universe

What we find is that the Universe was almost perfectly uniform back then, but some regions were more or less dense than average, by only 1-part-in-30,000. That's enough to grow into the stars, galaxies, galaxy clusters, and cosmic voids we see today. But these early imperfections that we see from this cosmic snapshot encodes an incredible amount of information about the Universe. One such piece of info is a startling fact: the curvature of space, as best as we can tell, is completely flat. If space were positively curved, like we lived on the surface of a 4D sphere, distant light rays would converge. If space were negatively curved, like the surface of a 4D saddle, distant light rays would diverge.

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