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Classical and quantum Cosmology of the S\'aez-Ballester theory

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arxiv 0904.0422 v1 pith:KNLFNBHE submitted 2009-04-02 gr-qc

J. Socorro , M. Sabido , L. Arturo Ureña-López This is my paper · ORCID
classification gr-qc
keywords theoryaez-ballesterapproachclassicalcosmologyexactmatterquantum
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We study the generalization of the S\'aez-Ballester theory applied to a flat FRW cosmological model. Classical exact solutions up to quadratures are easily obtained using the Hamilton-Jacobi approach. Contrary to claims in the specialized literature, it is shown that the S\'aez-Ballester theory cannot provide a realistic solution to the dark matter problem of Cosmology. Furthermore the quantization procedure of the theory can be simplified by reinterpreting the theory in the Einstein frame, where the scalar field can be interpreted as part of the matter content of the theory, in this approach, exact solutions are also found for the Wheeler-DeWitt equation in the quantum regime.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Power law scalar potential in the Saez-Ballester like theory: Exact solutions in the Bianchi type I case

    gr-qc 2026-04 unverdicted novelty 5.0 of 10

    Six exact anisotropic Bianchi I solutions in a two-scalar Sáez–Ballester–K-essence-like theory with inverse power-law potentials all approach a common late-time de Sitter attractor.

  2. Exact solutions using power law scalar potential in the Saez-Ballester-K-essence like theory

    gr-qc 2026-06 unverdicted novelty 4.0 of 10

    Exact Hamiltonian and Wheeler-DeWitt solutions for a hybrid Saez-Ballester K-essence model with V∼ϕ^{-λ} yield de Sitter-like late acceleration and a scalar field acting as cosmic background.

  3. Anisotropic power-law inflation for the S\'aez-Ballester theory non-minimally coupled to a vector field

    gr-qc 2025-02 conditional novelty 4.0 of 10

    A stable anisotropic inflationary solution exists in the Saez-Ballester theory, but it is equivalent to the known Kanno-Soda-Watanabe solution and has a too-large tensor-to-scalar ratio.

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