  We consider the growth rate of matter perturbations in the Einstein dark
energy theory. The theory consists of the Einstien-Hilbert Lagrangian plus the
trace of the energy momentum tensor, coupled non-minimally to a dynamical
vector field. We will show that the theory has three fixed points corresponding
to the dust, radiation and de Sitter universes. Due to the present of trace of
the energy-momentum tensor in the Lagrangian, the fixed points occurs in
different locations compared to $\Lambda$CDM theory. We will analyze the theory
with and without cosmological constant. We will fit the model parameters using
two independent data sets corresponding to the Hubble parameter $H$ and also
$f\sigma_8$. The theory is then shown to be consistent with observational data.
