= Solution
{c}
The <Friedmann-Lemaître-Robertson-Walker metric> implements the <cosmological principle>: on the scales being modelled, the spatial slices have <spatial homogeneity> and <cosmological isotropy>. There is a family of <comoving observers> whose orthogonal slices share one <cosmic time> and one <scale factor>. Each spatial slice is a <locally maximally symmetric space>, with time-independent normalized $k$.
The matter is represented by a <perfect fluid in general relativity>, at rest relative to the <comoving observers>, with <energy density> $\varrho(t)$ and <pressure> $p(t)$ depending only on <cosmic time>. Its <stress-energy tensor> is
$$
\boxed{T_{\mu\nu}=(\varrho+p)u_\mu u_\nu+p g_{\mu\nu},\qquad u=\partial_t.}
$$
There is no preferred spatial direction, so there is no <anisotropic stress> or spatial <heat flux> in that rest frame. Gravity obeys the <Einstein field equations>; the equations in this paper contain no separate <cosmological constant>, although a component with $p=-\varrho$ can represent one. An <equation of state> relating $p$ and $\varrho$ closes the evolution equations. <Spatial homogeneity> and <cosmological isotropy> are idealizations of the cosmological background; they do not assert that individual local structures are uniform.
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