Wave function of the Universe, Preferred reference frame effects and metric signature transition
Hossein Ghaffarnejad
备注：
4 pages (in letter format), 2 figures, Accepted to present ORALY at `4th International Conference on Mathematical Modeling in Physical Sciences, June 5-8, 2015, Mykonos, Greece`http://www.icmsquare.net/ and will be appeared in the conference proceeding book
发表信息：
Journal of Physics: Conference series 633 (2015) 012020
Gravitational model of non-minimally coupled Brans Dicke (BD) scalar field $ϕ$ with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter $V(ϕ)=Λϕ.$ Aim of the paper is to seek cosmological models which exhibit metric signature transition. The problem is studied in both classical and quantum cosmological approach with large values of BD parameter $ω>>1$. Scale factor of RW metric is obtained as $R(t)=6\sqrt{\frac{3}Λ}\cosh\big(\frac{t}{4}\sqrt{\fracΛ{3}}\big)$ which describes nonsingular inflationary universe in Lorentzian signature sector. Euclidean signature sector of our solution describes a re-collapsing universe and is obtained from analytic continuation of the Lorentzian sector by exchanging $t\to it$ as $R(t)=6\sqrt{\frac{3}Λ}\cos\big(\frac{t}{4}\sqrt{\fracΛ{3}}\big).$
Dynamical vector field together with the BD scalar field are treated as fluid with time dependent barotropic index. They have regular (dark) matter dominance in the Euclidean (Lorentzian) sector. We solved Wheeler De
Witt (WD) quantum wave equation of the cosmological system. Assuming a discrete non-zero ADM mass $M_j=4\sqrt{2}(2j+1)\sqrt{\fracΛ{3}}$ with $j=0,1,2,\cdots$, we obtained solutions of the WD equation as simple harmonic quantum Oscillator eigen functionals described by Hermite polynomials. Absolute values of these eigen functionals have nonzero values on the hypersurface $R=6\sqrt{\frac{3}Λ}$ in which metric field has signature degeneracy. Our eigen functionals describe nonzero probability of the space time with Lorentzian (Euclidean) signature for $R>6\sqrt{\frac{3}Λ}$ ($R<6\sqrt{\frac{3}Λ}$). Maximal probability corresponds to the ground state $j=0.$
As an alternative to dark matter models we use generalized Jordan-Brans-Dicke scalar-vector-tensor (JBD-SVT) gravity model to study the behavior of the rotational velocities of test particles moving around galaxies. To do so we consider an interaction potential $U(ϕ,N_μ)$ between the Brans-Dicke scalar field $ϕ$ and time like dynamical four-vector field $N_μ$ which plays as four velocity of a preferred reference frame. We show that at in weak field limits metric solution of the galaxy under consideration reaches to a modified Schwarzschild-de Sitter space in which mass of the vector field play…
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We expand on the idea that spacetime signature should be treated as a dynamical degree of freedom in quantum field theory. It has been argued that the probability distribution for signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is reviewed, and certain consistency constraints on the generalized signature (i.e. the tangent space metric $η_{ab}(x)=\mbox{diag}[e^{iθ(x)},1,1,1]$) are derived. It is shown that only one dynamical "Wick angle" $θ(x)$ can be introduced in the generalized signature, and the magnitude of fluctuation…
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A scalar bimetric theory of gravity with a preferred reference frame is summarized. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is found. Asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximation are built, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, hence the standard predictions of GR for photons are go…
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