Classical and quantum Bianchi type III vacuum Horava-Lifshitz cosmology

A diagonal Bianchi type III spacetime is treated, both at the classical and quantum level, in the context of Horava-Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the first kind. Closed form solutions are presented for various values of the coupling constants appearing in the action. Due to the method used, solutions of Euclidean, Lorentzian and neutral signatures are attained. The main general solution for lambda = 1 is seen to contain a curvature singularity at t = 0, while in its Einsteinian limit it reproduces the known diagonal solution (with and/or without cosmological constant). The rest of the solutions correspond to somewhat isolated cases, as they emerge from either setting the coefficient of the lapse to zero or taking lambda = 1/3. They are singularity free, but they all have a singular limit as the other constants approach their Einsteinian values. At the quantum level, the resulting Wheeler-DeWitt equation is explicitly solved for lambda = 1, sigma = 0 and lambda = 1/3 The ensuing wave functions diverge in the Einsteinian limit. (C) 2012 Published by Elsevier B.V.