Abstract:
In the first problem we investigate a model which incorporates spontaneous symmetry breaking and gravitation in the context of scalar-tensor theory. Present day value of the gravitational constant is induced by the vacuum expectation value of the scalar field. Cosmology is dominated by the scalar field both in the early and the present universe and the scalar field supplies the critical density of the universe today. In the second problem we applied the long-wavelength approximation to low energy effective string action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation is explicitly invariant under scale factor duality. We present the leading order general solution near a singularity, which also contains the quasi-isotropic one. The duality transformation is written as a coordinate transformation in an abstract space of fields.
