2018/09/15 by Alexander B. Balakin, Alexei S. Ilin
Engineering · Physics and Astronomy · #Coincidence #Cosmology and Gravitation Theories #Dark energy #Dark matter #Exact solutions in general relativity #Hubble's law #Material Science and Thermodynamics #Operator (biology) #Polynomial #Relativity and Gravitational Theory #Scale factor (cosmology) #Type (biology) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.3390/sym10090411
published as Symmetry, 2018, 10, 411 (1-16) · 15 pages, 0 figures, Invited paper for the Special Issue "Cosmological Inflation, Dark Matter and Dark Energy" of the Journal Symmetry (MDPI), Special Issue Editor: Kazuharu Bamba
arxiv created 2018/09/15 · openalex publication_date 2018/09/18 · arxiv updated 2018/09/19 · openalex created_date 2018/09/27 · openalex updated_date 2026/08/05
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.