Has there been any experiment trying to measure the Ricci Curvature of the universe? One of the major component of the Einstein equation is the Ricci Curvature. As of now, I understand it mathematically as some sort of trace of the Riemann Tensor, and geometrically as the factor by which volume disort as it travels through space.
My question is, has there been any experiment trying to measure the Ricci curvature in the universe? What did it find the Ricci Curvature function of the universe as?
 A: Simple Answer:
The Friedmann Equations comes from the EFE (Einstein Field Equations)
$$G_{\mu\nu} = \kappa T_{\mu \nu}$$
$$R_{\mu \nu} - \frac{1}{2}g_{\mu\nu}R= \kappa T_{\mu \nu}$$
Thus, when you measure the dynamics and evolution of the universe, you are kind of measuring the $R_{\mu\nu}$.
Long Answer:
As we know, the Ricci Tensor depends on the metric tensor. Considering different metric tensors will lead to different Ricci Tensor. For instance, if consider the FRW metric,
$$g_{\mu\nu}={\rm diag}(1, -\frac{a^2}{1-kr^2}, -a^2r^2, -a^2r^2\sin^2(\theta))$$
the $R_{\mu\nu}$ can be written as,
$$R_{00}  = -3\frac{\ddot{a}}{a}$$
$$R_{ij} = -[\frac{\ddot{a}}{a}+2(\frac{\dot{a}}{a})^2+2\frac{k}{a^2}]g_{ij}$$
We also know that, $$\frac{\dot{a}}{a} = H,~~\frac{\ddot{a}}{a} = -qH^2$$
By using these expressions, we can write $R_{\mu\nu}$ as
$$R_{00} = 3qH^2$$
$$R_{ij} = [qH^2 - 2H^2 - 2\frac{k}{a^2}]g_{ij}$$
From these cosmological parameters you can obtain some of the information about the Ricci Tensor. But in a sense measuring the Ricci Tensor is kind of measuring the dynamics of the universe since they make up the $G_{\mu\nu}$, which determines the dynamics of the universe.
