The probability of cosmic coincidence

The wave function of the quantum cosmological model of gravity coupled to a scalar field has been found at very early times. Corrections resulting from quadratic curvature terms may be evaluated and the functional dependence is found to have a similar form consistent with the inflationary epoch. The fundamental string theories would determine the gravitational action, and effective actions for both N = 1 and N = 2 string theories are examined, establishing a connection with topological string models. The nonlinear differential equation for the free energy of the 10-dimensional theory describing the compactification over a Calabi–Yau space of three complex dimensions is formulated, and it is transformed into a linear differential equation for the product of a function of the scaled string coupling and the partition function. A solution given by a sum over the genus is found for the series expansion of the partition function that can be matched in a bounded range for the coupling, and the scale factor, with the quantum cosmological wave function of the quadratic gravity model viable during the inflationary epoch.

Duke Scholars

Author Simon Wilton Davis Neurology, Translational Brain Sciences