Relationship Between Expansion and Curvature in the Universe

[Jaime Rudas]

TL;DR Summary

Is expansion a manifestation of curvature?

Orodruin said in another thread that "the spacetime of a spatially flat universe generally has curvature".

Is the expansion (or contraction) of a spatially flat universe the manifestation of the curvature of its spacetime?

If so, does the expansion correspond to a positive or negative curvature?

 

[Orodruin]

The behaviour of the scale factor is dependent on the energy content of the universe, which couples to the geometry through Einstein’s field equations. This contains the curvature through the appearance of the Einstein tensor. This is what results in the Friedmann equations.

 

[Orodruin]

Also note that curvature in general is described by a rank 4 tensor and not a single number. In the case of the homogeneous and isotropic spatial slices, the information can be boiled down to a single curvature invariant, but this is not generally the case.

Orodruin said in another thread that "the spacetime of a spatially flat universe generally has curvature".

Also, please use the mention feature if you refer to other users. Preceed the user name by an @ like this: @Jaime Rudas
In cases such as this you may also consider using the quote feature, where you can add quotes from several threads and then insert them into your post.

 

[weirdoguy]

using the quote feature, where you can add quotes from several threads and then insert them into your post.

Wow, finally after all these years I know what it's for Thanks.