On the effect of the degeneracy between w_0 and w_a

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter $w(z)$ and the fraction energy density $Ω_ϕ$. Based on the approximation, for slowly-rolling scalar fields, we derived the analytical expressions of $w(z)$ which reduce to the popular Chevallier-Polarski-Linder parametrization with explicit degeneracy relation between $w_0$ and $w_a$. The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among $w_a$, $w_0$ and $Ω_{m0}$. With the explicit degeneracy relations, we test their effects on the constraints of cosmological parameters. We find that: (1) The analytical relations between $w_0$ and $w_a$ for the two models are consistent with observational data; (2) The degeneracies have little effect on $Ω_{m0}$; (3) The $1σ$ error of $w_0$ was reduced about 30% with the degeneracy relations.

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