We derive new approximations for quintessence solutions that are simpler and an order of magnitude more accurate than anything available in the literature, which from an observational perspective \emph{ makes numerical calculations superfluous}. For example, our tracking quintessence approximation yields $\sim 0.1\%$ maximum relative errors of $H(z)/H_0$ and $\Omega_\mathrm{ m}(z)$ for the observationally viable inverse power law scalar field potentials, and similarly for viable thawing quintessence models using two slow-roll parameters. The approximations are trivially computed from the scalar field potential and as an application we give \emph{ analytic} expressions for the CPL parameters calculated from an arbitrary scalar field potential for thawing and tracking quintessence models.
Categories: gr-qc astro-ph.CO