Complete classification of Friedmann-Lemaitre-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics

We completely classify the Friedmann-Lemaitre-Robertson-Walker solutions with spatial curvature K = 0, +/- 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 (p.p.) 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.

Automated summary

In this paper, we classify the Friedmann-Lemaitre-Robertson-Walker solutions with spatial curvature K = 0, +/- 1 for perfect fluids with linear equation of state p = w rho without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated (p.p.) curvature singularities. Our study reveals that there are no non-null geodesics emanating from or terminating at the null portion of conformal infinity, and that the initial singularity for certain parameter ranges is a null non-scalar polynomial curvature singularity.