Speaker
Description
We study topological aspects of particle production using Stokes phenomenon. An explicit map between the standard $\beta$-coefficient computation, and Stokes constants from the perspective of the F-matrix formalism is presented. In scenarios where the particle dispersion relation reduces, in the long wavelength limit $(k\rightarrow 0)$, to the form $z^n$ $(n \in \mathbb{Z}_{>0})$ in complexified time coordinate $z$, the corresponding mode equation satisfies a $\mathbb{Z}_{n+2}$ symmetry. This symmetry, combined with the F-matrix formalism fixes the Stokes constants and the $\beta$ coefficient as a simple trigonometric function of $n$. In our on-going work we attempt to extend the above computation to small non-zero values of k by computing the lowest order correction to the Stokes constant for scenarios where the mode equation retains a $Z_{n+2}$ symmetry. These corrections are then used to estimate the topological contribution, corresponding to $k\approx 0$, to the total particle production in two scalar field models of interest for early universe cosmology.