1306.1827 (Hossein Ghaffarnejad)

Wave function of the Universe, preferred reference frame effects and
metric signature transition    [PDF]

Hossein Ghaffarnejad

Extending the Brans Dicke (BD) gravity theory in the presence of power-law self interacting potential $\thicksim\phi^n,$ action functional of a dynamical unit-time-like four vector field $N_{\mu}$ and action functional of perfect fluid matter field, we study classical and quantum approaches of a flat Robertson-Walker (RW) space time. In the classical approach we use slow-roll condition of the potential $V(\phi),$ and obtain power-law inflationary cosmological model which exhibits metric signature transition at the origin of time. Our solution follows $n\approx-4,$ with negative barotropic index $\gamma\approx-1$ corresponding to dark matter perfect fluid and $\omega\geq4\times10^4$ corresponding to the experimentally redicted value on the BD parameter. Deceleration parameter is obtained also as $q\approx-1.$ Applying a minisuperspace model of quantum cosmology, we derive corresponding Wheeler DeWitt (WD) wave functional equation of the system with a nonzero ADM mass. Minisuperspace potential of the WD equation has a saddle minimal point and near this point the WD takes a separable form. WD wave solution predicts a maximal probability on the metric signature transition hypersurface. Our WD wave solution follows $\omega\geq4\times10^4$ and slow-roll parameters of the self interacting BD potential which are used by our classical inflationary solutions. Furthermore our solutions predict a quantization condition on the ADM mass as $\mathcal{M}_{ADM}=k^2/l_p^2$ with $k=1,2,3,\cdots$ where $l_p=(16\pi G)^{1/2}$ is the well known Planck length.

View original: http://arxiv.org/abs/1306.1827