Spectral action for Robertson-Walker metrics

Abstract

We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a 6 against the known universal formulas of Gilkey and compute the expansion up to a 10 using our direct method. © SISSA 2012.