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Structure formation in generalized Rastall gravity

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Abstract

Recently, a modified version of Rastall theory of gravity has been introduced in which a varying coupling parameter could act as dark energy (DE) and thus, it can be held responsible for the current accelerated expansion of the Universe. Motivated by this modification, we study here the evolution of linear and nonlinear perturbations in the matter content of the Universe, utilizing spherically symmetric top-hat collapse scenario. The exact solutions we obtain in linear regime show that as the Universe evolves, matter density perturbations grow and reach a maximum value at a certain redshift after which these perturbations start decreasing toward a finite positive value at the present time. Depending on model parameters, exact oscillatory solutions can be also found representing that matter perturbations could experience either overdense and underdense regions during the dynamical evolution of the Universe. Numerical solutions in nonlinear regime show that the amplitude of perturbations grows much faster than the linear one and diverges at a critical redshift. However, the formation of collapsed structures is delayed as compared to \(\Lambda \)CDM model. It is found that the running mutual interaction between matter and geometry, encoded in the variable Rastall coupling parameter, could drastically affect the dynamics of matter perturbations and their growth rate during the evolution of the Universe.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author, [AHZ], upon reasonable request.]

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Acknowledgements

The authors would like to appreciate the anonymous referee for providing useful comments and suggestions that helped us to improve the original version of our manuscript.

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Authors and Affiliations

  1. Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh, P.O. Box 55136-553, Maragheh, Iran

    A. H. Ziaie & H. Moradpour

  2. Physics Department, Faculty of Sciences, University of Sistan and Baluchestan, Zahedan, Iran

    H. Shabani

Authors
  1. A. H. Ziaie
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  2. H. Moradpour
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  3. H. Shabani
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Correspondence to A. H. Ziaie.

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Ziaie, A.H., Moradpour, H. & Shabani, H. Structure formation in generalized Rastall gravity. Eur. Phys. J. Plus 135, 916 (2020). https://doi.org/10.1140/epjp/s13360-020-00927-2

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