Density fluctuations in $\kappa$-deformed inflationary universe

TL;DR

This paper investigates how $ppa$-deformation affects the spectrum of metric fluctuations during inflation, revealing non-trivial corrections and potential explanations for observed CMB anomalies.

Contribution

It introduces a non-local theory of scalar metric fluctuations in $ppa$-deformed space and computes first-order corrections to the power spectrum for different inflation models.

Findings

Power spectra exhibit non-trivial time and momentum dependence corrections.

UV modes are weakly blue shifted early in inflation, decreasing over time.

Far-IR modes show a cutoff proportional to $k^3$, possibly explaining low CMB quadrupole.

Abstract

We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $\kappa-$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $\kappa-$deformation. We expand the non-local action in $H^2/\kappa^2$, with $H$ being the Hubble parameter and $\kappa$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/\kappa^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.