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We completely classify the Friedmann-Lema\^{i}tre-Robertson-Walker solutionswith spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation ofstate $p=w\rho $, where $\rho$ and $p$ are the energy density and pressure,without assuming any energy conditions. We extend our previous work to includeall geodesics and parallelly propagated curvature singularities, showing thatno non-null geodesic emanates from or terminates at the null portion ofconformal infinity and that the initial singularity for $K=0,-1$ and$-5/3<w<-1$ is a null non-scalar polynomial curvature singularity. We thusobtain the Penrose diagrams for all possible cases and identify $w=-5/3$ as acritical value for both the future big-rip singularity and the past nullconformal boundary.

classical and quantum gravity

Complete classification of Friedmann-Lema\^{i}tre-Robertson-Walker  solutions with linear equation of state: parallelly propagated curvature  singularities for general geodesics