We investigate the interacting dark energy models by using the diagnostics of
statefinder hierarchy and growth rate of structure. We wish to explore the
deviations from ΛCDM and to differentiate possible degeneracies in the
interacting dark energy models with the geometrical and structure growth
diagnostics. We consider two interacting forms for the models, i.e., Q1=βHρc and Q2=βHρde, with β being the dimensionless
coupling parameter. Our focus is the IΛCDM model that is a
one-parameter extension to ΛCDM by considering a direct coupling
between the vacuum energy (Λ) and cold dark matter (CDM), with the only
additional parameter β. But we begin with a more general case by
considering the IwCDM model in which dark energy has a constant w
(equation-of-state parameter). For calculating the growth rate of structure, we
employ the "parametrized post-Friedmann" theoretical framework for interacting
dark energy to numerically obtain the ϵ(z) values for the models. We
show that in both geometrical and structural diagnostics the impact of w is
much stronger than that of β in the IwCDM model. We thus wish to have a
closer look at the IΛCDM model by combining the geometrical and
structural diagnostics. We find that the evolutionary trajectories in the
S3(1)--ϵ plane exhibit distinctive features and the departures
from ΛCDM could be well evaluated, theoretically, indicating that the
composite null diagnostic {S3(1),ϵ} is a promising tool for
investigating the interacting dark energy models.Comment: 17 pages, 4 figures; accepted for publication in JCA