Is there an imprint of Planck scale physics on inflationary cosmology?

TL;DR

This paper investigates whether quantum gravitational effects at the Planck scale influence inflationary cosmology, finding that such effects do not significantly alter the primordial power spectrum or produce distinguishable signatures in the CMBR.

Contribution

It introduces a model that considers arbitrary initial states and dispersion relations, showing these factors do not significantly affect the inflationary power spectrum.

Findings

Power spectrum largely independent of dispersion relation

Deviations from scale invariance are indistinguishable from standard inflation

Quantum gravitational effects do not produce observable signatures in CMBR

Abstract

We study the effects of the trans-Planckian dispersion relation on the spectrum of the primordial density perturbations during inflation. In contrast to the earlier analyses, we do not assume any specific form of the dispersion relation and allow the initial state of the field to be arbitrary. We obtain the spectrum of vacuum fluctuations of the quantum field by considering a scalar field satisfying the linear wave equation with higher spatial derivative terms propagating in the de Sitter space-time. We show that the power spectrum does not strongly depend on the dispersion relation and that the form of the dispersion relation does not play a significant role in obtaining the corrections to the scale invariant spectrum. We also show that the signatures of the deviations from the flat scale-invariant spectrum from the CMBR observations due to quantum gravitational effects cannot be differentiated from the standard inflationary scenario with an arbitrary initial state.