  We completely classify the Friedmann-Lema\^{i}tre-Robertson-Walker solutions
with spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation of
state $p=w\rho $, where $\rho$ and $p$ are the energy density and pressure,
without assuming any energy conditions. We extend our previous work to include
all geodesics and parallelly propagated curvature singularities, showing that
no non-null geodesic emanates from or terminates at the null portion of
conformal infinity and that the initial singularity for $K=0,-1$ and
$-5/3<w<-1$ is a null non-scalar polynomial curvature singularity. We thus
obtain the Penrose diagrams for all possible cases and identify $w=-5/3$ as a
critical value for both the future big-rip singularity and the past null
conformal boundary.
