| Popis: |
We completely classify Friedmann-Lema\^{i}tre-Robertson-Walker 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 $\rho < 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $\rho>0$, while no big-bang singularity for $w<-1$ and $\rho>0$. For $K=0$ or $-1$, $-10$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w<-1$ and $\rho>0$, with null geodesics being future complete for $-5/3\le w<-1$ but incomplete for $w<-5/3$. For $w=-1/3$, the expansion speed is constant. For $-1-1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1Comment: 37 pages, 8 figures, minor correction, accepted for publication in Classical and Quantum Gravity |
