Gravity-Driven Acceleration and Kinetic Inflation in Noncommutative Brans-Dicke Setting

By assuming the spatially flat~FLRW line-element and employing the Hamiltonian formalism, a noncommutative (NC) setting of the Brans-Dicke (BD) theory is introduced. We investigate gravity-driven acceleration and kinetic inflation in this NC BD cosmology. Despite to the commutative case, in which both the scale factor and BD scalar field are obtained in power-law forms (in terms of the cosmic time), in our herein NC model, we see that the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on not only the NC parameter but also the momentum conjugate associated to the BD scalar field. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome the problems within the standard BD cosmology in a more efficient manner. Moreover, we see that a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the NC parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.