Power Spectrum with Auxiliary Fields in de Sitter Space

Abstract

We use the auxiliary fields and (excited-) de Sitter solutions to study the standard power spectrum of primordial fluctuations of a scalar field in the early universe. The auxiliary fields are the negative norm solutions of the field equation and as it is shown, with a fixed boundary condition, utilizing these states results in a finite power spectrum without any infinity. The power spectrum is determined by the de Sitter solutions up to some corrections and the space-time symmetry is not broken in this point of view. The modulation to the power spectrum is of order $ (\frac{H}{\Lambda})^{2} $, where $ H $ is the Hubble parameter and $ \Lambda $ is the energy scale, e.g., Planck scale.