In-in'' formalism and cosmological perturbations

We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the in-in'' formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the primordial spectrum. We show that diagrams with two or more vertices require careful handling. We present an implementation of the operator formalism in which these diagrams can be evaluated in a simple and transparent fashion. We illustrate our methodology by evaluating the correction to the primordial gravitational wave spectrum generated by scalar loops, a 2-vertex, 1-loop interaction. We then look at a generalized N-point, 2-vertex diagram.