Statefinder hierarchy: An extended null diagnostic for concordance cosmology

Abstract

We show how higher derivatives of the expansion factor can be developed into a null diagnostic for concordance cosmology (ΛCDM). It is well known that the Statefinder – the third derivative of the expansion factor written in dimensionless form, a (ᶟ) /aH ᶟ , equals unity for ΛCDM. We generalize this result and demonstrate that the hierarchy, a (ᴺ) /aH ᴺ , can be converted to a form that stays pegged at unity in concordance cosmology. This remarkable property of the Statefinder hierarchy enables it to be used as an extended null diagnostic for the cosmological constant. The Statefinder hierarchy, combined with the growth rate of matter perturbations, can serve as a composite null diagnostic to differentiate between dark energy models.