Self-interaction in a cosmic dark fluid: The four-kernel rheological extension of the equations of state

Alexander B. Balakin and Alexei S. Ilin
Phys. Rev. D 105, 103525 – Published 18 May 2022

Abstract

We establish a new self-consistent model of coupling between the cosmic dark energy and dark matter in the framework of the rheological approach, which is based on the representation of the equations of state in terms of integral operators of the Volterra type. We elaborate on the so-called four-kernel model, in the framework of which both the dark energy and dark matter pressures are presented by two integrals containing the energy densities of the dark energy and dark matter. For the Volterra operators, the kernels of which are associated with the effects of fading memory, the corresponding isotropic homogeneous cosmological model is shown to be exactly integrable. We consider the classification of the model exact solutions, based on the analysis of roots of the characteristic polynomial associated with the key equation of the presented model. The scalars of the pressure and energy density of the dark energy and dark matter, the Hubble function and acceleration parameter are presented explicitly as the functions of the dimensionless scale factor. The scale factor as the function of the cosmological time is found in quadratures and is described analytically, qualitatively, and numerically. Asymptotic analysis allows us to classify the models with respect to behavior typical for the big rip, little rip, and pseudorip (de Sitter type). Two intriguing exact cosmological solutions are discussed, which describe the superexponential expansion and the symmetric bounce. New solutions are presented, which correspond to the quasiperiodic behavior of the state functions of the dark fluid and of the geometric characteristics of the Universe.

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  • Received 31 March 2022
  • Accepted 26 April 2022

DOI:https://doi.org/10.1103/PhysRevD.105.103525

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Alexander B. Balakin* and Alexei S. Ilin

  • Department of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya street 18, Kazan 420008, Russia

  • *Alexander.Balakin@kpfu.ru
  • alexeyilinjukeu@gmail.com

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Issue

Vol. 105, Iss. 10 — 15 May 2022

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