The scale factor in flat FRW model

[Orodruin]

Then I do not understand your point. There is nothing in GR prohibiting such global properties.

 

[TrickyDicky]

Then I do not understand your point. There is nothing in GR prohibiting such global properties.

Sorta, and yet:
http://en.wikipedia.org/wiki/General_covariance
"In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."

I guess you'll argue the global properties we are talking about are not "physical laws" but either "initial conditions" like homogeneity& isotropy, or local curvature, and there is a point in that because a metric is not a global physical law in GR, it is a "local law" so to speak. Still that local prescription has important physical consequences that seem to go counter the idea of coordinates playing no role "in the formulation of fundamental physical laws".

 

[Orodruin]

I guess you'll argue the global properties we are talking about are not "physical laws" but either "initial conditions" like homogeneity& isotropy, or local curvature, and there is a point in that because a metric is not a global physical law in GR, it is a "local law" so to speak. Still that local prescription has important physical consequences that seem to go counter the idea of coordinates playing no role "in the formulation of fundamental physical laws".

Local curvature is local, so this will be a local (and coordinate independent). Otherwise, something like that. Homogeneity and isotropy are global conditions that we are putting on the FRW universe. What local prescription are you suggesting has important physical quantities?

 

[TrickyDicky]

Local curvature is local, so this will be a local (and coordinate independent). Otherwise, something like that. Homogeneity and isotropy are global conditions that we are putting on the FRW universe. What local prescription are you suggesting has important physical quantities?

Curvature of the 4-manifold. Cosmology is a bit peculiar in this respect from other applications of GR, since one tries to infer from local curvature consequences for the whole universe and its evolution and origin, and despite the formal background independence of the theory.