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2007•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsRequires access

Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs spacetimes in scalar-coupled gravity theories

Uğur Camcı, Yusuf Kucukakca

Open publisher page 67 citations

Abstract

We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. We also find the explicit form of the scalar field in terms of the conformal time for Bianchi I, III, and Kantowski-Sachs models.

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What this paper is about

We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. We also find the explicit form of the scalar field in terms of the conformal time for Bianchi I, III, and Kantowski-Sachs models.

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OpenAlex reports 67 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. We also find the explicit form of the scalar field in terms of the conformal time for Bianchi I, III, and Kantowski-Sachs models.

Key concepts: Noether's theorem, Physics, Mathematical physics, Scalar field, Scalar (mathematics), Homogeneous space, Symmetry (geometry), Gravitation

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