Quantum Symmetries and Conserved Charges of the Cosmological Friedmann-Robertson-Walker Model

TL;DR

This paper explores the BRST and anti-BRST symmetries in the cosmological FRW model, deriving conserved charges and demonstrating their properties using supervariable approaches, thus deepening the geometric understanding of gauge symmetries in cosmology.

Contribution

It introduces a comprehensive geometrical description of BRST and anti-BRST symmetries in the FRW model via supervariable methods, including derivation of conserved charges and symmetry transformations.

Findings

Derived conserved (anti-)BRST charges using Noether's theorem.

Demonstrated nilpotency and anti-commutativity of these charges.

Established the geometrical framework of BRST symmetries in cosmology.

Abstract

We discuss both the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the cosmological Friedmann-Robertson-Walker (FRW) model with a differential gauge condition in the extended phase space. In this discussion, the presence of anti-BRST symmetry provides the complete geometrical description of BRST within the ambit of the supervariable approach. We derive the conserved (anti-)BRST charges for the FRW model using the celebrated Noether theorem and show the nilpotency and absolute anti-commutativity properties of these conserved charges within the realm of BRST formalism. Finally, we prove the sanctity of (anti-)BRST symmetries through the derivation of these symmetry transformations within the framework of the (anti-)chiral supervariable approach (ACSA) to BRST formalism.