Human knowledge has made a remarkable progress in modern history. One of its indicators is the unification of physical theories - different aspects of reality turn out to be manifestations of the same phenomena. Gravity was unified with astronomy, electricity with magnetism, electromagnetism with weak nuclear interactions. Nowadays, the most awaited is the unification of quantum theory and Einstein's gravity. Each step in the unification process requires the desertion of well-established schemes and gives rise to conceptual problems. Some of them result from theory's complexity and can be solved within it, others require a radical change of the paradigm. Both Einstein's and quantum theories suffer from conceptual problems: spacetime singularities, cosmological constant, wave function collapse,... The hoped-for unified theory of quantum gravity will necessarily lead to even more dramatic conceptual difficulties, as the very notions of point, time or causality become obscure. In the project, we will fathom out the conceptual problems lurking in unification theories with the help of sophisticated tools of mathematical physics enriched by a philosophical reflection. In particular, we hope to lift the veil on the following questions: Is dark energy, which according to the current cosmological model constitutes 68% of the Universe, only an artefact of Einstein's theory's complexity? What happens to the notions of time and space at the level of quantum gravity? How can one understand the cause-effect relation in physical regime, in which the notion of time becomes blurred? We expect that an in-depth analysis of these questions will shed new light on the long-standing problems in physics and pave the way to new testable effects. This would broaden our understanding of the fundamental aspects of Nature. Rigorous scientific research will be accompanied by popular lectures and articles aimed at the popularisation of modern physical theories among the wide audience.