The Statefinder hierarchy: An extended null diagnostic for concordance cosmology

Understand

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.