The FRW metric is given by: $$ds^2=-dt^2+a^2(t)\ dr^2$$ where $ds$ is an interval of proper length, $dt$ is an interval of cosmic time, $dr$ is an interval of co-moving co-ordinate distance and $a(t)$ is the scale factor (also $c=1$).
If I take $dt=0$ then I find that an interval of proper distance $ds$ is given by: $$ds = a(t)\ dr$$
Thus the proper distance between two nearby co-moving points is proportional to the scale factor - space expands.
If I take $ds=0$ then I obtain the null geodesic equation describing the path of a light ray: $$dt = a(t)\ dr$$
Thus the light travel time between two nearby co-moving points is also proportional to the scale factor.
Does this imply that intervals of cosmic time expand along with intervals of space?
The natural clocks in co-moving co-ordinates are expanding light-clocks.
Maybe in order to derive the constant units of the "atomic" time that we experience, $d\tau$, from expanding cosmic time intervals $dt$, we need to use the conformal time equation: $$d\tau = dt/a(t)$$
