New simple and accurate approximations for quintessence

We derive new simple approximations for quintessence in a spatially homogeneous, isotropic and flat spacetime. The approximations are typically an order of magnitude more accurate than anything available in the literature, which from an observational perspective makes numerical calculations superfluous. For example, our tracking quintessence approximation, with one less parameter than CPL and a comparably simple expression, yields a $0.1%$ maximum relative error of H(z)/H₀ for the inverse power law scalar field potential. We situate the new results in a broader dark energy context, where the present parametrized deviations from ΛCDM offer simple alternatives to the CPL parametrization, useful for observations at increasingly large redshifts.