Parity at the Planck scale

TL;DR

This paper investigates how parity symmetry might be fundamentally altered at the Planck scale, leading to superpositions of states and potential observable effects in cosmological data, within a formal framework and specific $ppa$-Poincare9 models.

Contribution

It introduces a formalism for parity at the Planck scale that allows for non-traditional behaviors and applies it to $ppa$-Poincare9 kinematics, highlighting potential observational signatures.

Findings

Parity may generate superpositions of right and left states at the Planck scale.

Different power spectra for tensor modes could indicate deformed parity symmetry.

Scale-invariance and parity symmetry are deeply interconnected at the Planck scale.

Abstract

We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum ${\bf k}$: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by $\kappa$-Poincar\'e symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected.