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

Abstract

We completely classify the Friedmann-Lemaître-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.

arXiv comment21 pages, 7 figures, major revision, published in Class. Quantum Grav

References in corpus (18)

• Planck 2015 results. XIII. Cosmological parameters
• Cosmological Imprint of an Energy Component with General Equation of State
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• Phantom Energy and Cosmic Doomsday
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Gravitational Vacuum Condensate Stars
• Horndeski theory and beyond: a review
• Stable gravastars - an alternative to black holes?
• Threshold of primordial black hole formation
• Phantom cosmologies
• Singularity Theorems and Their Consequences
• Classification of cosmological milestones
• Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion
• Complete conformal classification of the Friedmann-Lemaitre-Robertson-Walker solutions with a linear equation of state
• Maximal extensions and singularities in inflationary spacetimes
• Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes
• Degeneracy of the b-boundary in General Relativity

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