Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

TL;DR

This paper investigates how quantum gravitational effects, modeled via path integral duality, introduce Planck scale corrections to the primordial density spectrum during exponential inflation, finding scale-independent modifications proportional to the ratio of inflationary to Planck scales.

Contribution

It applies the principle of path integral duality to evaluate Planck scale corrections to the primordial spectrum in exponential inflation, highlighting scale-independent effects.

Findings

Corrections are of order (H/M_P)

Corrections are scale-independent

Implications for early universe cosmology

Abstract

The enormous red-shifting of the modes during the inflationary epoch suggests that physics at the Planck scale may modify the standard, nearly, scale-invariant, primordial, density perturbation spectrum. Under the principle of path-integral duality, the space-time behaves as though it has a minimal length $L_{_{\rm P}}$ (which we shall assume to be of the order of the Planck length), a feature that is expected to arise when the quantum gravitational effects on the matter fields have been taken into account. Using the method of path integral duality, in this work, we evaluate the Planck scale corrections to the spectrum of density perturbations in the case of exponential inflation. We find that the amplitude of the corrections is of the order of $({\cal H}/M_{_{\rm P}})$, where ${\cal H}$ and $M_{_{\rm P}}$ denote the inflationary and the Planck energy scales, respectively. We also find that the corrections turn out to be completely independent of scale. We briefly discuss the implications of our result, and also comment on how it compares with an earlier result.