https://doi.org/10.1140/epjp/s13360-024-05010-8
Regular Article
Anticommuting (anti-)BRST symmetries in FLRW model: supervariable approach
1
Department of Physics, Institute of Applied Sciences and Humanities, GLA University, 281406, Mathura, Uttar Pradesh, India
2
Department of Physics, Siksha Bhavana, Visva-Bharati, 731235, Santiniketan, Bolpur, West Bengal, India
Received:
4
November
2023
Accepted:
15
February
2024
Published online:
29
February
2024
Friedmann–Lema
tre–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 
-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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
