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.

 

[sardar]

I can understand your confusion regarding the Ricci scalar and the curvature of the FRW metric. Let me explain it in simpler terms. The FRW metric is a mathematical representation of the homogeneity and isotropy of our universe on a large scale. This metric has a constant, represented by the letter 'k', which determines the curvature of space. This constant can take on values of 1, 0, or -1.

Now, the Einstein equations are a set of equations that describe the relationship between the curvature of space and the energy and matter present in the universe. The Ricci scalar is a mathematical quantity that is derived from these equations and is used to measure the curvature of space at a specific point in time.

It is important to note that the curvature of space is not constant, it can change over time. This is why the Ricci scalar is a function of time in the FRW metric. The Friedman equation, which is derived from the Einstein equations, relates the curvature of space to the energy and matter present in the universe.

In summary, the curvature of the universe is not constant, but it is described by a constant in the FRW metric. The Ricci scalar is a function of time and is used to measure the curvature of space at a specific point in time. I hope this helps clarify your confusion.