Is the Universe's Expansion Misinterpreted Due to Curvature?

[PK is a fool]

TL;DR

Hi guys,
I don't have a clue what I am talking about really but have been thinking about the exponential expansion of the universe. I just thought that if the universe was actually curved positively, that the redshift phenomenon would be observed at an accelerating rate due to the surface of a sphere increasing even if that sphere is actually expanding at a constant or even in a state of deceleration.
I hope that you can put my mind at ease with a simple answer.

I hope that I am conveying what I see in my head clearly. I guess that I am visually imagining the 3 spatial dimensions projected on the 2d surface of a sphere and as that sphere expands that the increased distance between 2 points would happen what seems like at an accelerating rate because of geometry. Like if the radius of the sphere itself was increasing at a constant rate, that the distancd between 2 points on the circumference would increase at a faster and exponential rate.
Could the expansion of the universe actually be constant or even decelerating, but just observed on a curved path as an increased redshift of light v distance due to curvature?
I hope that this makes some sort of sense and please be kind with your responses. I think about this stuff all the time and this the first time I'm asking anyone else about something.

 

[Arman777]

Summary::

Could the expansion of the universe actually be constant or even decelerating, but just observed on a curved path as an increased redshift of light v distance due to curvature?

So are you asking that Universe is not accelerating but the curvature of the universe effects redshift ? So that it seems to us universe is expanding ?

 

[Bandersnatch]

Hi PK, and welcome.

Like if the radius of the sphere itself was increasing at a constant rate, that the distancd between 2 points on the circumference would increase at a faster and exponential rate.

The circumference of a sphere is $2\pi R$. More generally, the length of an arc along the circumference is $\theta R$, where $\theta$ is arc angle in radians. I.e., the distance between any two points on the surface of a sphere grows linearly with its radius, not exponentially.

In any case, expansion of the universe concerns behaviour of distances within the universe (i.e. on the surface of the sphere in this analogy). If the distances are observed to be growing, then they're growing. Whatever happens in higher-dimensions that may or may not exist does not affect the observation that's already been made.

 

[PeterDonis]

Could the expansion of the universe actually be constant or even decelerating, but just observed on a curved path as an increased redshift of light v distance due to curvature?

The short answer is, no.

The slightly longer answer is, when cosmologists say the expansion of the universe is accelerating, they are not talking about "raw" direct observations. They are talking about a conclusion they have come to after looking at not just the raw data but the best current model of the universe that that data leads us to. That best current model, when making predictions about things like observed redshifts of light from distant galaxies, already takes into account the spacetime geometry, and therefore includes all effects of spacetime curvature on the paths of light rays and their brightness.