Four Momentum in an Isotropic and Homogeneous Universe

We define the four-momentum of a particle by $p^mu = (E, mathbf{p})$, where $E$ is energy and $mathbf{p}$ the three momentum of the particle. In cosmology, we conventionally use the Friedmann-Robertson-Walker (FRW) metric to describe an isotropic and homogeneous Universe. Note that here I’ve scaled the quantities so that $c = frac{h}{2pi} = 1$.

I was told in lectures that the assumptions of isotropy and homogeneity meant that $partial_i P^mu = 0$. Can someone explain clearly why this is?