The Power Spectrum in de Sitter Inflation, Revisited

TL;DR

This paper revisits the de Sitter inflation power spectrum, proposing a new definition based on vacuum amplitude differences, which can significantly alter the predicted fluctuation amplitude.

Contribution

It introduces a redefinition of the physical power spectrum as a vacuum amplitude difference, linking it to the inflaton mass and revisiting quantum fluctuation predictions.

Findings

Amplitude of quantum fluctuations matches between vacua.

Redefining power spectrum reduces its amplitude based on inflaton mass.

Scale-free spectrum persists despite amplitude change.

Abstract

We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.