On the Dependence of the Spectra of Fluctuations in Inflationary Cosmology on Trans-Planckian Physics

TL;DR

This paper investigates how the initial conditions set by trans-Planckian physics at a critical length scale influence the inflationary power spectrum of metric fluctuations, revealing dependence on the new physics scale and initial vacuum choices.

Contribution

It introduces a framework for calculating inflationary spectra with initial conditions at a trans-Planckian scale, highlighting how different assumptions affect the results.

Findings

Power spectrum deviations depend on the ratio of inflationary Hubble rate to new physics scale.

Different vacuum choices lead to fractional differences in the spectrum.

Results vary for density fluctuations and gravitational waves.

Abstract

We calculate the power spectrum of metric fluctuations in inflationary cosmology starting with initial conditions which are imposed mode by mode when the wavelength equals some critical length $\ell_{_{\rm C}}$ corresponding to a new energy scale $M_{_{\rm C}}$ at which trans-Planckian physics becomes important. In this case, the power spectrum can differ from what is calculated in the usual framework (which amounts to choosing the adiabatic vacuum state). The fractional difference in the results depends on the ratio $\sigma_0$ between the Hubble expansion rate $H_{\rm inf}$ during inflation and the new energy scale $M_{_{\rm C}}$. We show how and why different choices of the initial vacuum state (stemming from different assumptions about trans-Planckian physics) lead to fractional differences which depend on different powers of $\sigma_0$. As we emphasize, the power in general also depends on whether one is calculating the power spectrum of density fluctuations or of gravitational waves.