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Varying vacuum models with spatial curvature: a dynamical system perspective

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Abstract

We investigate the qualitative cosmic dynamics of varying vacuum models with the non-flat, homogeneous and isotropic background. In these models, the dark matter interacts with the vacuum energy. We utilize the dynamical system technique to explore the existence and stability of fixed points. The existence of radiation and matter dominated decelerating phase of the universe may be explained in these models. The accelerating universe expansion may also be explained due to the existence of an attractor in these models. Further, the numerical solution technique is incorporated to solve the autonomous systems. These solutions are utilized to illustrate the evolution of cosmographic and statefinder parameters along with the energy conditions. The Milne universe solution exists in the model which is a consequence of spatially curved geometry. The stability criterion of the fixed points reveals that the cosmic history in the considered models may be observationally viable. Furthermore, the strength of interaction terms are constrained using the observational estimates of the cosmographic parameters.

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Acknowledgements

We are grateful to the honorable reviewer for highlighting different issues of the manuscript, which have been helpful to modify the manuscript. AS acknowledge the support of IUCAA, Pune under the Visiting associateship programme. AS also acknowledge the facilities under ICARD of IUCAA, Pune in the GLA University, Mathura. AS acknowledge the support of University of Zululand, South Africa where a part of this paper has been completed.

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Authors and Affiliations

  1. Centre for Cosmology, Astrophysics and Space Science, GLA University, Mathura, Uttar Pradesh, 281406, India

    Ashutosh Singh

  2. Department of Mathematical Sciences, Faculty of Science, Agriculture and Engineering, University of Zululand, Kwadlangezwa, 3886, South Africa

    Syamala Krishnannair

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  1. Ashutosh Singh
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  2. Syamala Krishnannair
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A. Singh: Conceptualization, Writing—original draft, Formal analysis, Review and editing. S. Krishnannair: Formal analysis, Review and editing.

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Correspondence to Ashutosh Singh.

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Singh, A., Krishnannair, S. Varying vacuum models with spatial curvature: a dynamical system perspective. Gen Relativ Gravit 56, 31 (2024). https://doi.org/10.1007/s10714-024-03219-7

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