Is there a known parametrization for time dilation in the FLRW metric?

[PeterDonis]

if an observer is in relative motion to the fundamental observer and to the fundamental observer the universe is homogeneous and isotropic. Am I correct in thinking that the com-moving observer would not see the universe as isotropic?

What you are calling the "fundamental observer" is what is usually called a "comoving observer". Those observers see the universe as homogeneous and isotropic. An observer in relative motion to the comoving observer in his vicinity will *not* see the universe as homogeneous and isotropic.

 

[Mordred]

thanks that's what I thought but wanted to make sure