Re-parameterization Invariance of FRW Model: Supervariable and BRST Approaches

TL;DR

This paper applies advanced BRST quantization techniques to a cosmological FRW model, revealing re-parameterization invariance, establishing BRST-anti-BRST symmetries, and demonstrating the universal nature of CF-type restrictions in quantum cosmology.

Contribution

It introduces the first application of the modified Bonora-Tonin supervariable approach to a physical one-dimensional cosmological system, deriving novel BRST-anti-BRST symmetries and CF-type restrictions.

Findings

Established nilpotent BRST-anti-BRST symmetries for the FRW model.

Derived the BRST-anti-BRST invariant CF-type restriction.

Proved the universal nature of CF-type restrictions across models.

Abstract

We perform the Becchi-Rouet-Stora-Tyutin (BRST) quantization of a $(0 + 1)$-dimensional cosmological Friedmann-Robertson-Walker (FRW) model. This quantization leverages the classical infinitesimal and continuous re-parameterization symmetry transformations of the system. To derive the nilpotent re-parameterization invariant BRST-anti-BRST symmetry transformations for the scale factor and corresponding momentum variables present in the cosmological FRW model, we employ the modified Bonora-Tonin supervariable approach (MBTSA) to BRST formalism. Through this approach, we also establish the BRST-anti-BRST invariant Curci-Ferrari (CF)-type restriction for this cosmological re-parameterization invariant model. Further, we obtain the off-shell nilpotent quantum BRST-anti-BRST symmetry transformations for other variables within the model using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of ACSA, the CF-type restriction is demonstrated through two key aspects: $(i)$ the invariance of the coupled Lagrangians under symmetry transformations, and $(ii)$ the absolute anti-commutativity of the conserved BRST-anti-BRST charges. Notably, applying the MBTSA to a physical cosmological system, specifically a one-dimensional one, constitutes a novel contribution to this work. Additionally, in the application of ACSA, we restrict our analysis to (anti-)chiral super expansions of supervariables, leading to the unique observation of the absolute anti-commutativity of the conserved BRST-anti-BRST charges. Moreover, we highlight that the CF-type restriction demonstrates a universal nature, remaining consistent across any re-parameterization invariant models in general D-dimensional spacetime.