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Zach Weinersmith

Hey cosmolo...don

Why does Inflation imply that the universe is flat? The usual analogy given is that if you're on the surface of Earth and it suddenly rapidly expands, it'd look flat. I don't get this analogy.

Like, wouldn't that also be true if the expansion were gradual? Also, and I'm sorry if this is especially stupid, but... the Earth's surface is closed not flat. Anyone have a better explanation?

30 Mar 2023 at 13:30 | Open on mastodon.social
31 comments
Keegan Leech
Adriano
ds

@ZachWeinersmith there's actually a theory for this, just google "sonic inflation" for more info

30 Mar 2023 at 13:33 | Open on wetdry.world
Zalasur đŸ”

@ZachWeinersmith I actually haven't heard that particular analogy. The closest I've heard is that at small scales a flat universe would be indistinguishable from a closed or open one because the curvature would be locally undetectable.

I think you might be referring to *spacetime* which is a four dimensional manifold existing in a theoretical five dimensional space. An accelerating universe would be curved in that context even if the physical universe itself were flat.

30 Mar 2023 at 13:35 | Open on mastodon.surazal.net
Zalasur đŸ”

@ZachWeinersmith (full disclosure: I'm not a scientist or even a mathematician. I'm just an enthusiastic amateur who's spent an awful lot of time reading about such matters) 😉

30 Mar 2023 at 13:38 | Open on mastodon.surazal.net
Zalasur đŸ”

@ZachWeinersmith Reading your original post maybe what they were trying to convey is that with rapid expansion, you'd find yourself going from a locally curved space to a locally flat one in a hurry. It's hard to say since it's an unfamiliar analogy to me but that's my guess

30 Mar 2023 at 13:42 | Open on mastodon.surazal.net
Paul Quirk

@ZachWeinersmith except doesn't the fact that light has a measurable speed and does not move infinitely fast suggest the universe is curved?

30 Mar 2023 at 13:39 | Open on mastodon.social
Rich Holmes

@quirk @ZachWeinersmith No, light speed has nothing to do with space curvature.

Yes, a gradual expansion would *eventually* give you curvature so small it's indistinguishable from flat. But you need the expansion to be rapid for it to have flattened early enough in the history of the universe.

It would still not be absolutely flat, it could be open or closed, but on such a huge scale (vastly larger than the observable universe) you couldn't tell it isn't flat.

30 Mar 2023 at 14:06 | Open on vmst.io
Paul Quirk

@doctroid @ZachWeinersmith then why does light have a measurable speed from our perspective?

30 Mar 2023 at 14:12 | Open on mastodon.social
Rich Holmes

@quirk @ZachWeinersmith Nothing can have infinite speed. That would mean an action here has immediate consequences infinitely far away. The universe doesn't work like that.

30 Mar 2023 at 14:25 | Open on vmst.io
Paul Quirk

@doctroid @ZachWeinersmith Einstein's theory of relativity describes time dilation as someone near the speed of light experiences time differently from an observer on earth; a few minutes for them could be a few hours for us. If you were to travel at the speed of light, you'd think your trip was instantaneous, while a great deal of time would have passed on earth. Speed = distance / time, if you divide by 0 you get ∞. We don't observe this, so light must be bending in our universe of space time.

30 Mar 2023 at 14:44 | Open on mastodon.social
Rich Holmes

@quirk @ZachWeinersmith As someone with a doctorate in physics, I can tell you your understanding is incorrect. For one thing, nothing prior to the last sentence has anything to do with curvature, so the last sentence doesn't follow. And we do observe light behaving in exactly the way you describe, curvature or no curvature.

30 Mar 2023 at 15:47 | Open on vmst.io
Paul Quirk

@doctroid @ZachWeinersmith your argument from authority notwithstanding, general relativity does tell us that, from the perspective of light, it travels instantly. From our perspective, it does not. We understand this as time dilation. So how do you account for the fact that light does have an observable speed limit in our universe from all perspectives other than light? Or has this theory been superseded?

30 Mar 2023 at 16:09 | Open on mastodon.social
Oblomov

@quirk
The finiteness of the speed of light suggests that _spacetime_ is hyperbolic rather than Euclidean, but it tells us nothing about the curvature of space.

@ZachWeinersmith

30 Mar 2023 at 14:45 | Open on sociale.network
Paul Quirk

@oblomov @ZachWeinersmith except for the fact that, as light travels through space, its vector is being changed from the straight line at infinite speed it wants to travel at to a vector where we observe it travelling at 299 792 458 m/s, which is the universal speed of light. It's folly to dismiss this interaction when determining the shape of the universe, as this may give us a clue as to both the size and shape of the universe.

30 Mar 2023 at 15:43 | Open on mastodon.social
DR

@ZachWeinersmith
It helps to think about inflation as actually shrinking what you think of as the observable/contactable universe. In the Earth analogy, if you can see out to a large enough distance, the curvature of the Earth is visible. What inflation does is take the local region around you, which looks flat, and stretches it out to fill your zone of visibility. The initial curvature of the Earth hasn't gone away, it's just not relevant to you any more - likewise our observable space slice looks flat.

Re other q:

Roughly speaking, during (slow-roll) inflation, the energy density of the inflation field is basically constant, i.e. it acts like dark energy today, although much more "impactful". So unlike radiation and matter, which dilute away as 1/a^4 and 1/a^3 respectively (where a is the scale factor of the expansion), the inflation energy density stays fixed during the expansion (increasing a) and overcomes the curvature term in the Hubble equation, which dilutes away as 1/a^2.

@ZachWeinersmith
It helps to think about inflation as actually shrinking what you think of as the observable/contactable universe. In the Earth analogy, if you can see out to a large enough distance, the curvature of the Earth is visible. What inflation does is take the local region around you, which looks flat, and stretches it out to fill your zone of visibility. The initial curvature of the Earth hasn't gone away, it's just not relevant to you any more - likewise our observable space slice looks flat.

30 Mar 2023 at 14:07 | Open on universeodon.com
DR

@ZachWeinersmith To elaborate further, one of the big selling points of inflation is that it explains why the universe looks so close to being spatially flat today, despite the fact that you would expect a non-zero curvature to be very much more likely. The way inflation takes care of this is to say that, whatever the initial (or primordial) curvature in the universe (positive or negative), space will expand so rapidly that a small region of space that is initially flat soon becomes the entire observable universe.

The added benefit of this is that it also explains another issue, which is why the universe looks so uniform/the temperature of the CMB is basically the same everywhere. Without inflation, it means that regions that could never have been in contact with each other (via speed of light signals) coordinated to look the same. With inflation, the universe looks the same because it was initially some very small region (in good thermal contact with itself) that expanded ~e^60 times

@ZachWeinersmith To elaborate further, one of the big selling points of inflation is that it explains why the universe looks so close to being spatially flat today, despite the fact that you would expect a non-zero curvature to be very much more likely. The way inflation takes care of this is to say that, whatever the initial (or primordial) curvature in the universe (positive or negative), space will expand so rapidly that a small region of space that is initially flat soon becomes the entire observable universe.

30 Mar 2023 at 14:36 | Open on universeodon.com
DR

@ZachWeinersmith Just to clarify a couple of points

- We model spacetimes and spatial slices as manifolds, so that at small enough scales, they look like flat spacetime and space respectively

- The uniformity issue arises because we take the universe to be finite in age, so without inflation there just hasn't been enough time for antipodal points in the celestial sphere to show the same CMB temperature -- at the beginning of the universe, they would have been causally disconnected and no signal could have reached one from the other by today

@ZachWeinersmith Just to clarify a couple of points

- We model spacetimes and spatial slices as manifolds, so that at small enough scales, they look like flat spacetime and space respectively

- The uniformity issue arises because we take the universe to be finite in age, so without inflation there just hasn't been enough time for antipodal points in the celestial sphere to show the same CMB temperature -- at the beginning of the universe, they would have been causally disconnected and no signal could...

30 Mar 2023 at 14:45 | Open on universeodon.com
DR

@ZachWeinersmith

Just one more:

Going back to the Earth analogy, imagine you were at the top of a mountain, standing on a flat rectangular carpet with a fancy design. You are high enough up that you can see the curvature of the Earth. The effect of inflationary expansion is to basically stretch out your rectangular carpet to the horizon, so it looks like the whole world is just flat-carpet land, and the carpet pattern is everywhere you look. The curvature of the Earth, all the landmarks in the distance are far far beyond what you can see.

@ZachWeinersmith

Just one more:

Going back to the Earth analogy, imagine you were at the top of a mountain, standing on a flat rectangular carpet with a fancy design. You are high enough up that you can see the curvature of the Earth. The effect of inflationary expansion is to basically stretch out your rectangular carpet to the horizon, so it looks like the whole world is just flat-carpet land, and the carpet pattern is everywhere you look. The curvature of the Earth, all the landmarks in the distance...

30 Mar 2023 at 14:55 | Open on universeodon.com
hjhornbeck

@ZachWeinersmith Not a cosmologist, but I’ll give this a crack.

Speed is a red herring here, you’re correct to note that scale is the only important factor.

Ever done calculus? At each point of a well-behaved continuous function, you can draw a tangent. That tangent will always be perfectly flat, no matter how curvy the function is, because that’s what “well-behaved continuous” means: zoom in closer and closer at any point, and it looks more and more flat.

Spacetime, according to GR, is also “well-behaved continuous.” Pick any point, and the more you inflate/scale the overall space, the more that point resembles its derivative. The local area “flattens out,” no matter how curved the original space was.

@ZachWeinersmith Not a cosmologist, but I’ll give this a crack.

Speed is a red herring here, you’re correct to note that scale is the only important factor.

Ever done calculus? At each point of a well-behaved continuous function, you can draw a tangent. That tangent will always be perfectly flat, no matter how curvy the function is, because that’s what “well-behaved continuous” means: zoom in closer and closer at any point, and it looks more and more flat.

30 Mar 2023 at 14:09 | Open on freethought.online
Ed Seedhouse

@ZachWeinersmith

The Earth is only curved in three dimensions. The universe would be curved or flat in four dimensions. I think it's likely a mistake to generalize from three to four dimensions.

30 Mar 2023 at 14:17 | Open on babblebox.net
Ast

@VA7SDH @ZachWeinersmith
A 3D sphere is not just curved in 3D, it is impossible to map it to a flat 2D space. The sum of internal angles of triangles on its surface will not be 180°. A torus (= donut) on the other hand is curved in our 3D world, but _can_ be mapped to a flat, purely 2D surface. It would be like a computer game where you enter the screen from the left as you enter from the right or fall from the top as you fall through the bottom.

30 Mar 2023 at 14:38 | Open on mastodon.social
Ed Seedhouse

@ast0815 @ZachWeinersmith

I already know all that, so what's your point?

If a sphere in three space is expanded sufficiently, any practicable measurement taken on it's surface will be indistinguishable from the same measurement taken on an infinite 2D surface.

30 Mar 2023 at 15:09 | Open on babblebox.net
Hyolobrika
Knut MorÄ

@ZachWeinersmith Being flat is unstable-- an accelerated expansion will expand more when it is bigger and a closed universe will collapse faster the more it has collapsed, so if the expansion is too gradual, the universe will run away from flatness too fast

@wild mind checking my work :D?

30 Mar 2023 at 14:45 | Open on snabelen.no
Matthijs

@kdund @ZachWeinersmith you're basically describing the flatness problem: general relativity predicts that different sources of energy form a delicate balance, described by the Friedmann equation. As the universe expands, the density of matter and radiation decrease, and curvature (being a source of energy in GR) should dominate over time. This is not what is observed. Inflation solves this by having the inflaton field provide the difference.

30 Mar 2023 at 15:42 | Open on mas.to
rich

@ZachWeinersmith I've never liked or got the "bug walking on a balloon" analogy and it's variants😡

30 Mar 2023 at 15:00 | Open on mastodon.gamedev.place
Ed Seedhouse

@ZachWeinersmith

If the Earth were expanded to, say, a radius of 1 million light years while we remain the same size, how could any practicable measurement taken on the surface be distinguished from the same measurement taken on an completely flat surface?

30 Mar 2023 at 15:14 | Open on babblebox.net
DELETED

@ZachWeinersmith Inflation is important because it happens faster than the speed of light, so the points in spacetime can't talk to each other while they're inflating. If they can't talk to each other, they can't transfer energy, and energy causes clumping and thus gravity because of General Relativity. Gravity *is* non-zero curvature.

30 Mar 2023 at 16:00 | Open on masto.chronos-tachyon.net
DELETED

@ZachWeinersmith I'm sure there's an excellent episode of PBS SpaceTime on the subject if you prefer your physics in the form of a YouTube video.

30 Mar 2023 at 16:00 | Open on masto.chronos-tachyon.net
DELETED

@ZachWeinersmith There are also some other considerations between local curvature and global curvature that I've glossed over, but it's really heavily tied in to how GR works.

For instance, if a 2-sphere like Earth's surface increases in size, the local curvature becomes more flat but the global curvature remains positive no matter how large the sphere is. Surfaces with positive global curvature like a sphere's surface are always finite, while surfaces with flat or negative global curvature can be infinite. GR, however, lets you take a non-zero global curvature and "inflate it away" so that you are causally disconnected from being able to detect the non-zero curvature. The global curvature remains the same, but because the local curvature at any point is so close to zero, you would need to see outside your light cone to detect it in the CMB (the most distant thing you can see). A universe with slow inflation and non-zero curvature would show non-180° triangles in the CMB, for instance.

@ZachWeinersmith There are also some other considerations between local curvature and global curvature that I've glossed over, but it's really heavily tied in to how GR works.

For instance, if a 2-sphere like Earth's surface increases in size, the local curvature becomes more flat but the global curvature remains positive no matter how large the sphere is. Surfaces with positive global curvature like a sphere's surface are always finite, while surfaces with flat or negative global curvature can be...

30 Mar 2023 at 16:29 | Open on masto.chronos-tachyon.net
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