(Anti-)BRST Symmetries in FLRW Model: Supervariable Approach

TL;DR

This paper derives and analyzes the (anti-)BRST symmetry transformations for the FLRW cosmological model using supervariable formalism, highlighting the role of horizontality and CF-type conditions in ensuring symmetry properties.

Contribution

It introduces a consistent supervariable approach to derive off-shell nilpotent (anti-)BRST symmetries for the FLRW model, connecting diffeomorphism invariance with BRST formalism.

Findings

Derivation of (anti-)BRST transformations using supervariables

Identification of CF-type condition as key to symmetry properties

Construction of BRST-invariant quantum Lagrangians

Abstract

Friedmann-Lemaitre-Robertson-Walker (FLRW) model, representing the isotropic and homogeneous Universe, has an inherent diffeomorphism (or reparametrization) invariance. For a given local time-reparametrization symmetry transformation of (0+1)-dimensional (1D) diffeomorphism invariant FLRW model, we derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations in a consistent manner. The supervariable approach to BRST formalism is used as a guiding tool in finding the proper (anti-)BRST transformations. An application of (super-)diffeomorphism invariance, in the context of superspace formalism, yields horizontality conditions. Moreover, the celebrated CF-type condition which is universal for 1D diffeomorphism invariant theories, emerges as an off-shoot of the horizontality condition and provides the absolute anticommutativity of the (anti-)BRST transformations. In addition, this CF-type condition leads to the derivation of coupled (but equivalent) (anti-)BRST invariant quantum Lagrangians for FLRW model. We also capture the geometrical interpretation of the (anti-)BRST transformations and their properties in terms of the Grassmannian translational generators and supervariables.