LRS Bianchi type I universes exhibiting Noether symmetry in the scalar-tensor Brans-Dicke theory

Following up on hints of anisotropy in the cosmic microwave background radiation data, we investigate locally rotational symmetric Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and an arbitrary function. We illustrate with families of examples designed to be generalizations of the well-known power-expansion, exponential expansion and Big Rip models in the Friedmann-Robertson-Walker framework. The solutions display surprising variation, a large subset of which features late-time acceleration as is usually ascribed to dark energy (phantom or quintessence), and is consistent with observational data.