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My name is Tom. I am just learning about space and physics and how the universe works.

I have a question and I am not sure if I am posting it in the correct place or not so please let me know if I am posting it wrongly.

My question is about gravities relationship with the expansion of the universe.

The question is that could empty space be curved?

By this I mean either:

1) Can there be a gravitational field that permiates the universe as a whole. Maybe from the sum of small ( negligable effects ) multiplied over the numerous massive of the universe, dark matter, or using brane theory ... a source from outside our brane.

2) That space just has a natural 4d curve to it.

Now for number one above. If all of the matter in the universe has an effect on every single point in the universe ( even if it is negligable ) then at each point all forces would roughly even out so the direction of the gravitational pull would not exist, however the effect of the red shift would work.

Now the questions remains how much gravity would be needed to create the redshift needed for this effect. Since the curvature near a massive object greatly offsets the effects of universal expansion, I think the amount of curvature throughout space needed to produce the redshift should be within reason.

My question is how can I calculate the amount of gravity that would be needed?

How can I test this?