Relationship between Energy density and Curvature

Question

I don't know GR so while answering the question so keep in mind that.

In the Friedmann Equations, is energy density has an effect on curvature or vice versa? Or they are separate things and they don't affect each other?

For example can we have an energy density $\rho_0$ such that its less then a critical density $\rho_c\,,\,\,(\rho_0<\rho_c)$ in a positive curvature universe ?

Or a hyperbolic universe with $\rho_0>\rho_c$. In general, it seems it should affect, but I couldn't be sure.

G. Smith · Accepted Answer · 2019-01-13T17:48:44.617

1

The Einstein field equations relate the components of spacetime curvature to the density and flow of energy and momentum, somewhat similarly to how Maxwell’s field equations relate the electromagnetic field to the density and flow of electric charge.

Energy density and spacetime curvature are separate but related things. It is common to say that energy density “causes” curvature. However, you can have curvature in places where you don’t have energy density, just as in electromagnetism you can have electromagnetic field in places where you don’t have charge.

A homogeneous and isotropic universe can have positive, negative, or zero curvature. Zero curvature corresponds to a critical energy density, positive curvature to greater energy density, and negative curvature to lesser energy density.

edited Jan 13 '19 at 17:48

answered Jan 13 '19 at 17:29

G. Smith

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so my given examples are not possible ? – seVenVo1d Jan 13 '19 at 18:19
No, at least not in a homogeneous and isotropic universe. – G. Smith Jan 13 '19 at 18:22
So at the begining of the universe curvature and density values were fixed and never changes in that sense. – seVenVo1d Jan 13 '19 at 18:26
I believe it is true that a homogeneous and isotropic universe cannot evolve, for example, from positive to negative curvature. – G. Smith Jan 13 '19 at 18:37

Relationship between Energy density and Curvature

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