Mathematics – Logic
Scientific paper
Jan 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cqgra..27a5008g&link_type=abstract
Classical and Quantum Gravity, Volume 27, Issue 1, pp. 015008 (2010).
Mathematics
Logic
Scientific paper
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 '\skew3\tilde{\phi }', 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 'dt= \skew3\tilde{\phi }(\gamma )\,d\gamma'.
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