Our current fundamental description of interactions in the nature, based on the Standard Model of elementary particles (gauge quantum field theory) and the General Relativity (geometric theory), is neither satisfactory nor complete. There are theoretical problems which are considered to be, directly or indirectly, tied to our incomplete understanding of gravity. From the experimental viewpoint, the description is incomplete as it does not include or explain the dark matter. This project has the goal to improve the description and understanding of gravity, by analysing both its quantum and semi-classical domains.

Fundamental aspects will be studied through constructions and analyses of gauge theories with higher spins. Such theories generically contain spin-1 and spin-2 fields, and so are of unifying type. It is known that presence of an infinite tower of higher spin fields can drastically improve UV behaviour, so much that it may cure UV divergences of amplitudes which are present in Feynman perturbative calculus in standard quantum field theories. An example of a theory in which such behaviour is realised is the string theory. We shall also study interactions between matter and higher spin fields and analyse influence of nonlocal coupling to higher spin symmetries.

Semi-classical domain will be investigated through analyses of effective actions of quantised matter in the classical background consisting of standard gravity (spin-2) and also higher spin fields. Effect of quantum contributions on the solutions of the effective equations of motion will be analysed. As the these contributions are non-local, it is possible that they may produce qualitative changes on some solutions. Special attention will be directed to solutions describing black holes and cosmological ones. Quantum anomalies of gravitational origin will be studied, in particular recently discovered Pontryagin trace anomaly.