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In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these “paths or contamination” beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues.

This work is based on modification of the general relativity with two additional terms in the Einstein equations. The additional terms give macroscopic description of the quantum effects of production /absorption of matter by the vacuum. The theory (without fitting parameters and without hypothesis of inflation) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory, there is no Big Bang at the beginning, but some local bangs during the evolution are probable. Also, there is no critical density of the universe and, therefore, no dark energy (no need in the cosmological constant). Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of primary dark matter particles (possibly, gravitons) have started 43 billion years later. It is shown that characteristic distance between particles is much smaller than the thermal de Brogle wavelength, so that quantum effects, including formation of the Bose-Einstein condensate, can dominate, even for high temperature. "Ordinary" matter was synthesized from dark matter (with estimated small electric dipole moment (EDM)) in galaxies. Supplementary exact solutions are obtained for various ranges of parameters. From the theory we get an interface between dark and ordinary matter (IDOM), which very likely exist not only in cosmos, but everywhere, including our body and our brain. [ABSTRACT FROM AUTHOR]