A new generic evolution for $k$-essence dark energy with $w approx -1$. (arXiv:1905.05628v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Kehayias_J/0/1/0/all/0/1">John Kehayias</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Scherrer_R/0/1/0/all/0/1">Robert J. Scherrer</a>
We reexamine $k$-essence dark energy models with a scalar field $phi$ and a
factorized Lagrangian, $mathcal L = V(phi)F(X)$, with $X = frac{1}{2}
nabla_mu phi nabla^mu phi.$ A value of the equation of state parameter,
$w$, near $-1$ requires either $X approx 0$ or $dF/dX approx 0$. Previous
work showed that thawing models with $X approx 0$ evolve along a set of unique
trajectories for $w(a)$, while those with $F_X approx 0$ can result in a
variety of different forms for $w(a)$. We show that if $dV/dphi$ is small and
$(1/V)(dV/dphi)$ is roughly constant, then the latter models also converge
toward a single unique set of behaviors for $w(a)$, different from those with
$X approx 0$. We derive the functional form for $w(a)$ in this case, determine
the conditions on $V(phi)$ for which it applies, and present observational
constraints on this new class of models.
We reexamine $k$-essence dark energy models with a scalar field $phi$ and a
factorized Lagrangian, $mathcal L = V(phi)F(X)$, with $X = frac{1}{2}
nabla_mu phi nabla^mu phi.$ A value of the equation of state parameter,
$w$, near $-1$ requires either $X approx 0$ or $dF/dX approx 0$. Previous
work showed that thawing models with $X approx 0$ evolve along a set of unique
trajectories for $w(a)$, while those with $F_X approx 0$ can result in a
variety of different forms for $w(a)$. We show that if $dV/dphi$ is small and
$(1/V)(dV/dphi)$ is roughly constant, then the latter models also converge
toward a single unique set of behaviors for $w(a)$, different from those with
$X approx 0$. We derive the functional form for $w(a)$ in this case, determine
the conditions on $V(phi)$ for which it applies, and present observational
constraints on this new class of models.
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