Complete conformal classification of the Friedmann-Lemaître-Robertson-Walker solutions with a linear equation of state

We completely classify FLRW solutions with spatial curvature $K=0,\pm 1$ and equation of state $p=w\rho$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $\rho -1/3$ and $\rho>0$, while no big-bang singularity for $w 0$. For $K=0$ or $-1$, $-1 0$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w 0$, with null geodesics being future complete for $-5/3\le w -1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1

Keywords:

• Mathematical physics
• Cosmology
• Conformal map
• Linear equation
• Gravitational singularity
• Initial singularity
• Horizon
• Curvature
• Big Crunch
• Physics

• Correction
• Source
• Cite
• Save
• Machine Reading By IdeaReader