Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem

摘要: We study a new exactly solvable model of coupling the Dark Energy and Matter, in framework which kernel non-gravitational interaction is presented by integral Volterra-type operator well-known classical theory fading memory. Exact solutions this isotropic homogeneous cosmological were classified with respect to sign discriminant cubic characteristic polynomial associated key equation model. Energy-density scalars Hubble function acceleration parameter are explicitly; scale factor found quadratures. Asymptotic analysis exact has shown that Big Rip, Little Pseudo Rip regimes can be realized specific choice guiding parameters show Coincidence problem solved if we consider memory effect interactions Sector Universe.