A new approach to the vacuum of inflationary models

TL;DR

This paper introduces a novel boundary condition implementation for solving the Mukhanov-Sasaki equation in inflation, using a fitting function and finite conformal time, with applications to spectral index and tensor-to-scalar ratio constraints.

Contribution

It proposes a new method for boundary conditions in inflationary models, incorporating model-dependent fitting functions and finite conformal time boundary conditions.

Findings

Computed spectral index and its running for a specific inflationary model.

Constrained boundary condition parameters using observational bounds on tensor-to-scalar ratio.

Demonstrated potential generalizations of the method.

Abstract

A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might expect deviations from the standard approach to arise. The proposed method introduces a (model dependent) fitting function for the z"/z and a"/a terms in the Mukhanov-Sasaki equation for scalar and tensor modes, as well as imposes the boundary conditions at a finite conformal time. As an example, we employ a fitting function, and compute the spectral index, along with its running, for a specific inflationary model which possesses background equations that are analytically solvable. The observational upper bound on the tensor to scalar ratio is used to constrain the parameters of the boundary conditions in the tensor sector as well. An overview on the generalization of this method is also discussed.