Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem
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 homog...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/9/411 |
| _version_ | 1798041621174943744 |
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| author | Alexander B. Balakin Alexei S. Ilin |
| author_facet | Alexander B. Balakin Alexei S. Ilin |
| author_sort | Alexander B. Balakin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:24:02Z |
| format | Article |
| id | doaj.art-c42ee80e577a4308bc04b4fd2d922367 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:24:02Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c42ee80e577a4308bc04b4fd2d9223672022-12-22T03:59:56ZengMDPI AGSymmetry2073-89942018-09-0110941110.3390/sym10090411sym10090411Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence ProblemAlexander B. Balakin0Alexei S. Ilin1Department of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya str. 18, Kazan 420008, RussiaDepartment of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya str. 18, Kazan 420008, RussiaWe 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.http://www.mdpi.com/2073-8994/10/9/411Dark EnergyDark Mattermemory |
| spellingShingle | Alexander B. Balakin Alexei S. Ilin Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem Symmetry Dark Energy Dark Matter memory |
| title | Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem |
| title_full | Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem |
| title_fullStr | Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem |
| title_full_unstemmed | Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem |
| title_short | Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem |
| title_sort | dark energy and dark matter interaction kernels of volterra type and coincidence problem |
| topic | Dark Energy Dark Matter memory |
| url | http://www.mdpi.com/2073-8994/10/9/411 |
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