The Statefinder hierarchy: An extended null diagnostic for concordance
  cosmology
  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.
