Hamilton–Jacobi approach to cosmology with nonlinear sigma model

Abstract

We start with a short introduction of the role that constraints and Lagrange multiplers play in variational calculus. After recalling briefly the properties of the nonlinear sigma model, we show how the Hamilton–Jacobi method can be applied to find its solutions. We discuss the importance of the Hamiltonian constraint in the standard cosmological model, and finally, apply the Hamilton–Jacobi method to the solution of coupled gravitational and sigma-field equations.