Quantum cosmology with effects of a preferred reference frame

Abstract

Recently, we presented a gravity model by generalizing the Brans–Dicke theory which is suitable for studying the metric signature transition dynamics without using an imaginary time parameter. Adding a suitable scalar potential described in terms of the Brans–Dicke scalar field ‘’, this alternative theory is used to study the Wheeler–DeWitt approach of quantum cosmology. We assumed that the universe is defined in a flat Robertson–Walker metric with Lorentzian signature. In that case, the Wheeler–DeWitt wavefunctional is obtained as two-dimensional quantum harmonic oscillator convergent polynomials for both of the choices of positive and negative values of the Brans–Dicke parameter. Here we choose a preferred reference frame with a time coordinate of ‘γ’ which relates to time of cosmological free falling observer ‘t’ as ‘’.