The Statefinder hierarchy: An extended null diagnostic for concordance cosmology

TL;DR

The paper introduces an extended hierarchy of null diagnostics based on higher derivatives of the expansion factor, which remain at unity in LCDM, providing a tool to distinguish evolving dark energy from the standard model.

Contribution

It generalizes the Statefinder diagnostic to higher derivatives, creating a hierarchy that acts as an extended null diagnostic for concordance cosmology.

Findings

Hierarchy remains at unity for LCDM.

Enables differentiation between evolving dark energy and LCDM.

Combines with growth rate to form a composite diagnostic.

Abstract

We show how higher derivatives of the expansion factor can be developed into a null diagnostic for concordance cosmology (LCDM). It is well known that the Statefinder -- the third derivative of the expansion factor written in dimensionless form, a^{(3)}/aH^3, equals unity for LCDM. We generalize this result to higher derivatives of the expansion factor 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 defines a composite null diagnostic which can distinguish evolving dark energy from LCDM.