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

@article{Harada2018CompleteCC,
  title={Complete conformal classification of the Friedmann-Lemaitre-Robertson-Walker solutions with a linear equation of state},
  author={Tomohiro Harada and Bernard J. Carr and Takahisa Igata},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2018}
}
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… 
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