Ricci scalar and curveture of FRW metric

[sadegh4137]

hi

we know that our universe is homogenous and isotropic in large scale.
the metric describe these conditions is FRW metric.
In FRW, we have constant,k, that represent the surveture of space.
it can be 1,0,-1.
but the the Einstan Eq, Ricci scalar is obtained as function of time! and this leads to Frideman Eq.
I sonfuse about this. the curveture of universe is constant or not!

 

[TrickyDicky]

hi

we know that our universe is homogenous and isotropic in large scale.
the metric describe these conditions is FRW metric.
In FRW, we have constant,k, that represent the surveture of space.
it can be 1,0,-1.
but the the Einstan Eq, Ricci scalar is obtained as function of time! and this leads to Frideman Eq.
I sonfuse about this. the curveture of universe is constant or not!

You must make a distinction between the curvature of the spatial three dimensional hypersurface, that has constant curvature in the FRW universe, and the 4-dimensional spacetime curvature that doesn't have constant curvature in that model.

 

[sadegh4137]

yes i know
in The early universe is written by kolb in chapter 3
auther stayed that Ricci tensor in the special space is 6k/a(t)
I can't understand this!

 

[Bill_K]

"Constant curvature" means that the curvature of a space section is the same everywhere, i.e. independent of x,y,z. At a given instant, it's the same everywhere, like a sphere. In cosmological models the curvature of the space section varies with time.