Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosmology with positive and negative exponential potentials   We present a phase-plane analysis of cosmologies containing a scalar field
$\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$
where $\kappa^2 = 8\pi G$ and $V$ may be positive or negative. We show that
power-law kinetic-potential scaling solutions only exist for sufficiently flat
($\lambda^2<6$) positive potentials or steep ($\lambda^2>6$) negative
potentials. The latter correspond to a class of ever-expanding cosmologies with
negative potential. However we show that these expanding solutions with a
negative potential are to unstable in the presence of ordinary matter, spatial
curvature or anisotropic shear, and generic solutions always recollapse to a
singularity. Power-law kinetic-potential scaling solutions are the late-time
attractor in a collapsing universe for steep negative potentials (the ekpyrotic
scenario) and stable against matter, curvature or shear perturbations.
Otherwise kinetic-dominated solutions are the attractor during collapse (the
pre big bang scenario) and are only marginally stable with respect to
anisotropic shear.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: q-alg