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Description
Many cosmological models, which describe the global evolution of the Universe, include scalar fields. To describe only one epoch of the Universe evolution, single-field models can be used. Using two-field models, one can explore multiple epochs or multiple physical phenomena. Models with a single scalar field nonminimally coupled to gravity can be transformed to models with a minimally coupled scalar field with a canonical kinetic term by metric and scalar field transformations. On the other hand, it is not possible to transform a model with two scalar fields nonminimally coupled to gravity to a model with two minimally coupled scalar fields and a standard kinetic part of the Lagrangian in the most general case [1]. After the metric transformation, one obtains a general relativity model with non-standard kinetic terms of scalar fields, a so-called chiral cosmological model (CCM) [2].
To construct a new integrable CCM with two fields, we start from models with nonminimally coupled scalar fields. A similar single-field integrable model proposed in Ref. [3] has an interesting feature: the Ricci scalar is an integral of motion. Recently, N-field cosmological models with the same property have been found and their integrability in the spatially flat FLRW metric have been proven [4].
We find general solutions of evolution equations in the Friedmann universe with arbitrary spatial curvature for a few such two-field integrable models in a following manner: we show that in the conformal time, the system of the evolution equations can be transformed to a Hamiltonian system of two equations. For a few two-field polynomial potentials, we integrate this system and get analytic expressions of the general solutions in terms of the Jacobi elliptic functions. After finding such solutions, we obtain two-field chiral cosmological models in the Einstein frame by the conformal transformation of the metric. The obtained integrable CCMs have potentials represented in terms of hyperbolic functions.
The results of this work are presented in [4, 5].
References
[1] Kaiser D.I. Conformal Transformations with Multiple Scalar Fields // Phys. Rev. D. –– 2010. –– V. 81. –– P. 084044. –– arXiv:1003.1159 [gr-qc].
[2] Chervon S.V. On the chiral model of cosmological inflation // Russ. Phys. J. –– 1995. –– V. 38. –– P. 539–543.
[3] Boisseau B., Giacomini H., Polarski D., Starobinsky A.A. Bouncing Universes in Scalar-Tensor Gravity Models admitting Negative Potentials // JCAP. –– 2015. –– V. 07. –– P. 002. –– arXiv:1504.07927.
[4] Ivanov V.R., Vernov S.Y. Integrable Cosmological Models with an Arbitrary Number of Scalar Fields // Physics of Particles and Nuclei (to be published). –– 2025. –– arXiv:2407.05002.
[5] Ivanov V.R., Vernov S.Y. New Integrable Chiral Cosmological Models with Two Scalar
Fields // Phys. Rev. D. –– 2024. –– V. 110. –– arXiv:2407.12732.
| Тематическая секция | Гравитация и космология |
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