Abstract
We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the universe.
Highlights
Dark Matter (DM) and Dark Energy (DE) play the key roles in all modern cosmological scenaria
One of the motivation of this idea is connected with the so-called Coincidence Problem [18,19,20]), which is based on the fact that the ratio between DE and DM energy densities is nowadays of the order 73
The most known models are phenomenological; they operate with the so-called kernel of interaction, the function Q(t), which is linear in the energy densities of the DE and DM with coefficients proportional to the Hubble function [21]
Summary
Dark Matter (DM) and Dark Energy (DE) play the key roles in all modern cosmological scenaria (see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17], and references therein for the history of problem, for main ideas and mathematical details). The most known models are phenomenological; they operate with the so-called kernel of interaction, the function Q(t), which is linear in the energy densities of the DE and DM with coefficients proportional to the Hubble function [21]. In contrast to the known local phenomenological representations of the interaction kernels, the value of the source-function Q(t) in the model, which includes the Volterra integrals, is predetermined by whole prehistory of the Universe evolution. We consider the well-known two-fluid model, which describes the so-called Dark Fluid joining the DE and DM ; in this model the baryonic matter remains out of consideration
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