The Dark Energy Cosmic Clock: A New Way to Parametrise the Equation of State

Abstract

We propose a completely new parametrisation of the dark energy equation of state, which uses the dark energy density, $Ω_e$ as a cosmic clock. We expand the equation of state in a series of orthogonal polynomials, with $Ω_e$ as the expansion parameter and determine the expansion coefficients by fitting to SNIa and $H(z)$ data. Assuming that $Ω_e$ is a monotonic function of time, we show that our parametrisation performs better than the popular Chevallier--Polarski--Linder (CPL) and Gerke and Efstathiou (GE) parametrisations, and we demonstrate that it is robust to the choice of prior. Expanding in orthogonal polynomials allows us to relate models of dark energy directly to our parametrisation, which we illustrate by placing constraints on the expansion coefficients extracted from two popular quintessence models. Finally, we comment on how this parametrisation could be modified to accommodate high redshift data, where any non--monotonicity of $Ω_e$ would need to be accounted for.