Optimisation based algorithm for finding the action of cosmological phase transitions

We present the OptiBounce algorithm, a new and fast method for finding the bounce action for cosmological phase transitions. This is done by direct solution of the "reduced" minimisation problem proposed by Coleman, Glaser, and Martin. By using a new formula for the action, our method avoids the rescaling step used in other algorithms based on this formulation. The bounce path is represented using a pseudo-spectral Gauss-Legendre collocation scheme leading to a non-linear optimisation problem over the collocation coefficients. Efficient solution of this problem is enabled by recent advances in automatic differentiation, sparse matrix representation and large scale non-linear programming. The algorithm is optimised for finding nucleation temperatures by sharing model initialisation work between instances of the calculation when operating at different temperatures. We present numerical results on a range of potentials with up to 20 scalar fields, demonstrating O(1%) agreement with existing codes and highly favourable performance characteristics.