What is the physical meaning of Ricci scalar is a covariantly constant?

  • $\begingroup$ What exactly do you mean? To my mind, the Ricci scalar itself is a physical quantity and the physical meaning of it being (covariantly) constant is thus self-evident, i.e., it has the same value at all spacetime points. $\endgroup$
    – user87745
    Commented May 24, 2019 at 12:12
  • $\begingroup$ I guess he mean $\nabla_{\mu} \, R = 0$, which is true for the spatial section in an homogeneous spacetime. However, $R$ isn't a constant in the full spacetime. $R^{(3)} = \text{cste}$ is an expression of the homogeneity of the space section. $\endgroup$
    – Cham
    Commented May 24, 2019 at 13:01