On the Tensor Field Inflation in the GR Homogeneous Cosmological Model

The homogeneous cosmological model in GR is proposed, where the vacuum energy, which can cause the inflation, is described by tensor field rather than by commonly used in inflationary scenarios scalar field. It is shown that if the initial values of the field are sufficiently big (comparable with the Planck units), under the condition of the tensor field's slow change in the beginning the regime of the quasiexponential inflation can exist. Numerical solutions for the inflationary stage are obtained that confirm the validity of the approximate solutions. Inflation takes place under wide range of initial conditions provided that the tensor field satisfies the condition imposed on the initial values of the tensor field ${\phi^0}_0(0)\approx -{\phi^i}_i(0)$ (i=1,2,3). That condition also arises from the requirement to satisfy existing observational data.