Talk about the universe’s shape might sound like a weird concept, how can you define the shape of a 3-dimension space? And what does it mean? Well, the universe’s shape has very interesting implications for the cosmos, and for us as well.

#### Evolution on the cosmos view

Until the beginning of the 20th century, we used to have a totally different view of the universe. It was considered that our galaxy was unique, and this gigantic star cluster was surrounded by an infinite and empty space.

But with the observations made by Edwin Hubble in 1919, followed by the discovery of nebulae being distant galaxies beyond our milky way, followed by the observations of the universe’s expansion then years later; the image of our cosmos was radically changed.

Albert Einstein, along with its general theory of relativity, presented a mathematical model (Einstein’s field equations) that included this concept of expansion. Which he counteracted by adding a mathematical gimmick, the Cosmological constant (Λ). We have to remember that the theory of relativity was published in 1915, before the discoveries of Mr. Hubble. Einstein latter called this cosmological constant his “biggest blunder”.

Einstein’s equations have implications on how mass and energy interact and affect the space around it, which brought interesting questions. If mass and energy can change the space’s shape (this due its effect in the in the space-time); then, on a big scale, does the total mass and energy in the universe will influence its shape?

#### The universe’s shape.

Hubble ‘s discoveries, along with the Einstein’s general relativity, had two implications, first was that the universe had a beginning, fact that later was known as the “Big bang theory” (a phrase coined by astronomer Fred Hoyle, which ironically used as a pejorative concept, as Hoyle never consider this theory as valid). The second one was, of course, the shape of the universe.

In those models, space geometry depends on the energy and all the mass content in all the universe and, more precisely, on its average density or “Critical density” defined by the parameter “Ω” (Omega).

With key solutions like the Friedmann equations, who explain a homogeneous space expansion, the calculation can be made about the possible density of the universe; which comes in three possible shapes open, closed or flat; and to exemplify these shapes we can represent those in a two-dimension image and reflect its effect on a triangle.

But, why a triangle? Well, in school we learned that in Euclidean (flat), geometry a triangle’s inner angles adds 180 degrees, but if you alter the shape of the surface where this triangle is drawn, the sum of its angles will change, for example, in a triangle on the earth’s surface going from the equator to the north pole and back to the equator, the sum of its inner angles will add more than 180 degrees, given that this is not a Euclidean space.

But going back to the possible universe’s shapes, we mentioned three different scenarios:

A closed universe; with an energy density “Ω” above 1, which implies a spherical-like shaped universe, and in this case a triangle will have inner angles that add *more* than 180 degrees.

An open universe; with an energy density “Ω” below 1, which implies a hyperbolic geometry, similar to a horse saddle, and where a triangle will have inner angles that add *less* than 180 degrees.

A flat universe; with an energy density “Ω” equal to 1, implying a flat geometry, like a Euclidean plane, and where a triangle will have inner angles that are *equal* to 180 degrees.

This seems strange given that we speak of a three-dimensional space, how a three-dimensional space can be flat? Well, this is because we are biased since we live in a three-dimensional space, but to interpret this, I will quote an excellent explanation from one of my favorite astrophysicists and communicators.

#### How to understand dimensions

Dr. Neil Degrasse Tyson, Astrophysicist; explain in a very eloquent way how dimensions relate, this requires a bit of abstraction, so please, bear with me; Dr. DeGrass says…

A point is a zero- dimensional object.

A line is a one-dimensional object (it has length), bound by two zero- dimensional points.

A square is a two- dimension object (it has a surface), bound by four One-dimension lines.

A cube is a three- dimension object (it has volume), bound by six two-dimension squares.

And here’s where things become interesting, considering the fact that we live in a three-dimensional world. So far, we have noticed a progression, One-dimension line with two zero-dimensional points, two-dimension squares with four one-dimension lines, and so on.

So, we have a progression of two points, four lines, six squares. Two, four, six; this means that we add two items for each extra dimension we are evaluating. So, what if we want to know about higher dimensions? Then we have that…

A so-called “Tesseract or hyper-cube” is a four-dimension object, bound by eight three-dimensional cubes.

And we can continue with this progression…

“A five-dimensional object is that one that’s bound by ten four-dimension Tesseracts”.

And so on…

#### Flat universe

So, as explained before, when we say we are in a flat universe, we are referring to the flatness of a 3-D space. Yet still what does this represent? This fact is relatively easy to explain. In the simplest case of a flat universe, let’s say that you put two laser beams perfectly parallel among each other, in this case since the universe is flat these laser beams will remain parallel forever, “ad infinitum”.

However, for a closed, spherically shaped universe, the same perfect parallel laser beams, at some point in the distance will encounter each other, colliding, even when they were set perfectly parallel initially.

In the opposite scenario, in an open or a hyperbolic universe (saddle-like shaped), our laser beams, perfectly parallel to each, in the distant space will start to diverge from each other, having an increased distance between them the farther they go.

#### Well, what kind of space do we live in?

To determine this; astronomers and physicists tried first by weighing the universe, might sound weird, but with some dimension analysis they got some interesting values; yet, it is indeed really hard to quantify all the matter and energy in the universe; so they decide to try a different method, making use of a large triangle of cosmological size.

With a very generic explanation, astrophysicists used the source of more distant radiation in our universe, the Microwave Background Radiation, or CMB; the afterglow of the big bang, and probably one of the most important observations in cosmology history, this was the source that was used to do this measurement.

They created a triangle, using the observable features in the CMB, so in this way they could sort-of “draw” a triangle using these points; then, using simulations of the big bang and universe expansion they created reference images of how the CMB will look like for the three possible universe shapes; then they compared the simulations with the actual observed CMB and… it all seems to indicate, with a very high accuracy (0.4% margin of error), that the universe we live in is Flat.

#### And…, does it matter?

The universe’s shape has several interesting implications, but probably the most important is what the end of our universe will be like.

In the closed universe, at some point the universe expansion will stop, and then will be reversed; by the action of gravity all matter and energy will clump together again, in what is called a “big crunch”, an extremely hot implosion.

In the case of an open universe, the expansion will increase more and more, accelerating the process. And, in a similar case, on the flat universe, a continuous and never-ending expansion will remain; it will slow down but will never stop.

So, in our case, the fate of the universe doesn’t look good, with the space expansion, galaxies will be farther and farther from us, reaching a point where the expansion velocity will be so big that the light from other galaxies won’t be able to reach us. We will see only the stars in our milky way, nothing more; and it will look like we’re surrounded by a lonely and empty space. Space that will end up as a freezing cold and darker cosmos, where black holes will dominate the universe, and even these will disappear due the “Hawkins Radiation”, a sort of black hole evaporation. This has been called the “heat death”; also called the “Big freeze” or “Big rip”, because even the atoms will begin to disintegrate in this future.

But don’t fret, we still have time, the cosmos, with his 13.7 billion years, hasn’t reached its halfway point, Chinese scientists estimate that we are about 2 billion years from it, and then in another 16.7 billion years is when we will have the cosmos demise.

So, don’t sell your stock and max out your credit cards just yet!

Regards Alex – ScienceKindle!

I love the effort you put into writing this post, it helped me a lot in finding what I was looking for.

I can’t understand how the shape of universe can be flat, does this imply that all the observable stars are on same level (like disc shaped Milky Way) and not above or below us. I really thought it was spherical.

Can someone explain….

Hello:I think you need to check the details in this article.

“…in a flat universe, we are referring the flatness of a 3-D space. …, let’s say that you shoot two laser beams perfectly parallel among each other, in this case since the universe is flat these laser beams will remain parallel forever, “ad infinitum””. This means, the laser beams will never encounter or diverge from each other in a flat universe, no matter in which direction they are shoot.