Our universe is like any other object, and so has to have a shape. There are three possible shapes our universe can be:
Positively curved
Negatively curved
Perfectly flat
It's worth explaining here something that I should have clarified during my TikTok. In most scenarios when we think about curvature, we are visualising objects with two-dimensional surfaces. A tennis ball, for example, has a positively curved surface. A saddle has negative curvature, and the surface of a sheet of A4 paper appears flat. However, when talking about the curvature of the universe, we are actually referring to a "surface" in three dimensions (four in fact, if you count time!).
An object with a three-dimensional surface can still be flat, positively curved, or negatively curved. However, it's harder for us to visualise and even harder to demonstrate. I've drawn two sets of diagrams below, which show curvature on both 2D and 3D surfaces. I've also included the mathematical definitions of "flat", "positively curved" and "negatively curved", to try and make things a bit clearer:
There's an endless number of options for curvature, from slightly curved (think: saucer) to very curved (think: teacup). But only one option for flatness - flat! Therefore, the likelihood of the universe being flat is absolutely tiny. And yet... cosmologists are measuring the universe to be flat, to an accuracy of just 0.5%. To make matters even worse, calculations predict that the universe was flatter in the past!
Okay, time for another clarification."How can the universe be flatter in the past if there's only one option for flatness?" I hear you cry! An excellent question, and something else I should have made clear in my video. Essentially, if you run the Big Bang Model of the universe back in time, the accuracy of our flatness predictions actually increases...
To give you a like-for-like comparison, imagine you have a sheet of A4 paper, which appears almost entirely flat, but does, in fact, have edges that are 1mm higher than its centre. Next, you run the clock back until just a few minutes after the paper's creation (its own"Big Bang" if you will). However, now the paper's edges are not raised by 1mm. Instead, they measure at just one proton's diameter higher than the paper's middle!
So what could be the reason behind all of this flatness? Well, our current solution is a process called inflation, in which (we think) a little while after the big bang and in less than a fraction of a second, the universe rapidly expanded and flattened.
There isn't actually any irrefutable evidence for inflation currently, as such, but most scientists believe it had to have happened, otherwise our understanding of the universe starts to fall apart.
...Can you think of any other reason why our universe is incredibly flat?
The third and final clarification: I've had quite a few questions asking me why the universe has to be one of the three options listed above (positively curved, negatively curved, or flat). Why, for example, could it not be a mix of these three? This comes down to one of the foundations of cosmology - the cosmological principle.
The cosmological principle states that on large scales, the universe should be "isotropic" (i.e. appear the same in all directions) and "homogeneous" (i.e. have no preferred locations). Therefore, if the large-scale universe was positively curved in one region, and negatively curved in another, the cosmological principle would be broken!
Do note though, that the cosmological principle only applies to the large-scale universe. Planets, moons, stars and black holes (amongst lots of other things) warp space and change its curvature on the small scale all the time.
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