Bianchi I cosmology and scalar vector tensor Brans Dicke gravity

We consider Brans Dicke scalar vector tensor gravity to study an inflationary scenario of the accelerating expansion of the universe for which the anisotropy property occurs. We study both primordial inflation and late inflationary period of the universe. To do so we, use Bianchi I line element where spatial part has cylindrical symmetry along \(x\) direction in the local Cartesian coordinates. To seek stabilization of our obtained metric solution, we apply dynamical system approach to obtain critical manifolds in phase space and determine which of them confirms the inflation with stable nature in presence of the anisotropy property of spacetime. We solve dynamical equations for different directions of the timelike dynamical vector field. We obtain several critical manifolds whose nature of stable (sink) or quasi stable (saddle) are dependent on the direction of the used vector field. At last, we should point that observational constraint on the Brans Dicke parameter \(\omega>40000\) which satisfied by the well known Brans Dicke scalar tensor gravity is not valid for our modified scalar vector Brans Dicke gravity because of presence of timelike dynamical vector field.