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

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 $L_{{}_{\mathrm{P}}}$ (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 $(\mathcal{H}/M_{{}_{\mathrm{P}}})$, where $\mathcal{H}$ and $M_{{}_{\mathrm{P}}}$ 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.

12 pages, 1 figure, RevTex4 format

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• Path integral duality modified propagators in spacetimes with constant curvature
• Slow-roll reconstruction for running spectral index
• Szekeres Universes with GUP corrections