[onlyrealcuzzo]

How does the universe expand? What is it expanding into? And why isn't that thing considered the universe?

[SomewhatLikely]

Quoting Wikipedia: It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric governing the size and geometry of spacetime itself that changes in scale https://en.m.wikipedia.org/wiki/Expansion_of_the_universe

[onlyrealcuzzo]

What is the metric governing the size and geometry of spacetime? Gravity??

[bobbylarrybobby]

Gravity is not the metric, but it does interact with the metric (well, gravity is what we call it when mass or energy affects space time). The presence of mass/energy causes the shortest distance between two points to no longer be a straight path through space. The path an object takes through space time is always the path with the shortest space time interval among all paths (in that sense the path is “straight” the same way that in flat space, a straight line is the shortest path between two points) — this distance is given by the metric tensor — but gravity makes this path appear curved in space.

[drdeca]

The metric of the spacetime manifold. See https://en.wikipedia.org/wiki/Metric_tensor .

When you have a space that isn't just normal globally euclidean space (such as: on the surface of a sphere), the idea of a vector as in like "a direction you can go in and an amount of how much or how fast or whatever" isn't something that makes sense as something independent of a base location. Instead, each point in the space has associated with it a space of "tangent vectors" at that point, and these spaces are related to each other.

The metric tensor associates to each point a "bilinear form" with some properties, essentially a way of doing something like a dot product of two tangent vectors at that same point.

This in turn allows for defining the notion of the length of some curve through the manifold.

[ben_w]

Apparently it can be “loosely” thought of as such, but that implies there is some interesting difference way above my level: https://en.m.wikipedia.org/wiki/Metric_tensor_(general_relat...

[ben_w]

> What is it expanding into?

The future, literally. To grossly oversimplify: if all of space is east-west, and time is north-south, the Big Bang is the north pole. Only the universe is the map rather than the globe, and the globe doesn’t have to exist for the map to exist and to have the same expansion in space (/longitude) with respect to time (/latitude).

Also there may or may not be a Big Crunch/south pole, this is all just a way to get into the nature of the geometry by way of a convenient frame of reference.