A superspace description of Friedmann-Robertson-Walker models

TL;DR

This paper presents a superspace and BRST/BV formalism analysis of Friedmann-Robertson-Walker cosmological models, revealing their gauge structure and quantization properties in a superfield framework.

Contribution

It introduces a superspace approach with extended BRST symmetry and BV formalism to analyze FRW models, connecting gauge fixing, ghost terms, and quantum master equations.

Findings

Superfield structure reproduces gauge-fixing and ghost terms.

Extended BRST symmetry includes shift symmetry.

BV quantum master equation has a superfield formulation.

Abstract

We illustrate the cosmological Friedmann-Robertson-Walker (FRW) models realized as gauge theory in the extended configuration space with its Becchi-Rouet-Stora-Tyutin (BRST) invariance upto total derivative. To investigate the model in Batalin-Vilkovisky (BV) formalism the Lagrangian density of the models is further extended by introducing shifted fields corresponding to all fields. The extended Lagrangian density having shifted fields admits more general BRST symmetry (including shift symmetry), called as extended BRST symmetry. In this framework the antighost fields corresponding to the shift symmetry get identified with antifields of BV formulation. Further, we analyse the models on supermanifold with the help of additional super (Grassmannian) coordinate $\theta$. Remarkably, we observe that the $\theta$ components of superfields produces the gauge-fixing term in tandem with ghost term of the effective Lagrangian density naturally. Furthermore, we show that the quantum master equation of the BV quantization method can be translated to have a superfield structure for the FRW models.