He developed a new method for studying the composition of primary particles of ultrahigh-energy cosmic radiation and obtained restrictions on the composition of primary particles with energies 10¹⁸ – 10²⁰ eV and higher, in including the world's most stringent restrictions on the flux of primary photons with such energies;fotonom;

correlations with the positions of cosmologically distant active galaxies of a certain class, which cannot be explained within the framework of the Standard Model, are found in data on the directions of arrival of ultrahigh-energy cosmic rays, and an experimentally verifiable explanation is proposed in terms of a new light pseudoscalar particle mixing with a photon;

within the framework of theories with additional spatial dimensions, he proposed a natural explanation of the hierarchical mass structure and mixing of fermions of three generations, based on a model with a number of parameters less than the number of fitted quantities - the only model in which the hierarchies of charged fermions and neutrinos are naturally explained by one mechanism, and model predictions can be tested in current and future experiments, including at the Large Hadron Collider;

explanation of the anomalous transparency of the Universe for high-energy gamma radiation, as well as the observed gamma radiation in the TeV range from the gamma-ray burst GRB 221009A has been proposed;

a new scientific program of the Carpet experiment at the Baksan Neutrino Observatory has been developed; the concept of a new generation axion helioscope in Troitsk TASTE has been formulated, which became the basis of the Baby-IAXO experiment

He made a fundamental contribution to the development of the theory of tunnel transitions with a change in spatial topology in quantum gravity, proposed to consider a massive graviton as a candidate for the role of dark matter; he (with co-authors) proposed a formalism that allows calculating changes in the state of quantized fields occurring during such transitions, discovered and quantitatively described a number of non-trivial effects, such as topological birth of particles in a conformally flat metric, non-conservation of global quantum numbers, possible violation of quantum coherence; a decisive contribution was made to solving the problem of the probability of tunneling processes (in particular, anomalous non-conservation of the baryon number and the decay of a false vacuum) in particle collisions at high energies; a generalization of the quasi-classical formalism has been developed for the first time, which makes it possible to calculate the corresponding cross-sections in theories with weak coupling, the possibility of numerical calculation of probabilities is shown, a conclusion is made about the exponential smallness of the cross-sections of such processes in collisions of high-energy particles; known results have been obtained in the study of the properties of extended objects in field theory, such as strings in models with a nontrivial space of modules and nontopological solitons, in the field of theories with additional dimensions of space.

He and his co–authors have shown that active galactic nuclei of a certain type – the so-called lacertides - are likely sources of ultrahigh-energy cosmic rays; it has been determined that compact astronomical objects can collapse as a result of their capture of dark matter; the strictest restrictions on the prevalence of primary black holes and models of weakly interacting massive dark matter particles have been obtained based on measurements of the Faraday rotation of radiation from remote radio sources, a model of the Galaxy's magnetic field, widely used at present, is constructed.