Hubble's Law, Friedman Models & Spacetime Curvature Explained

[Tahmeed]

Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?

 

[Jorrie]

Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?

Any non-static spacetime (expanding or contracting) is always curved, so yes, the linear distance-recession rate relation (Hubble's law) always holds. The distance-redshift relation is non-linear and depends on the curvature of space (the spatial curvature-density parameter).