Einstein, Planck and Vera Rubin: relevant encounters between the Cosmological and the Quantum Worlds

The phenomenal roles in investigating the Universe and its content and governing rules, of these three great scientists is without discussion. However, despite that we have today a well organized system of laws of Nature and a formidable set of experimental and observational discoveries, the status of the Universe seems to require that researchers in Observational Cosmology, General Relativity and Quantum Physics concur together and join forces in building new effective paths of knowledge. In fact, it is well known that about $95\%$ of the energy density of the Universe is of dubious invisible nature and cannot be framed within the "presently verified" physics. Moreover, a number of phenomena like e.g. "inflation", "matter-antimatter asymmetry", "cosmological and astrophysical quantum relativistic objects" , " dark matter" just to name a few, are far from being understood and good ideas like "the Unification of Gravity with the other forces" and "the intrinsic Symmetry of the Universe" are also stalling. In these circumstances, conceptually new directions of investigation have been proposed. The Universe is considered not only as the arena where theories (on, e.g. ,Dark Matter) get falsified/verified, but, through the properties of its content, a strong motivator for creating of totally new ones. A contamination among Cosmology, Astrophysics, Relativity , Theoretical Physics, Physics of the Elementary particles theory is taking place in many recent investigations aimed to discover the new Physics. This is the leitmotiv of the Special Topic collection to which this work belongs; we want to contribute to it by providing a review of 15 examples of such new paths of contaminated knowledge. This review, of course, is not complete in presenting this kind of current investigations, but this shortcoming is much alleviated by considering the references of this work and expecially the other works of this Special Topic collection.