Matter perturbations in Einstein dark energy model

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.