Research interests

Scientific interests include quantum field theory, quantum gravity and cosmology, and their applications in the physics of the early and modern universe.

In a wide class of field models, Andrei developed covariant methods for calculating the quantum effective action and the core of the heat equation underlying it, for which a covariant perturbation theory in powers of space-time curvature was constructed. He owns important results on the quantization of gauge-invariant constrained systems, including the operator realization of quantum Dirac constraints, their solution in the form of a path integral, semiclassical approximation, and applications to the Wheeler-DeWitt equation in quantum cosmology.

One of the main areas of activity is the study of the problem of the quantum origin of the early Universe, including the problem of quantum initial data for its inflationary stage. In particular, a quantum cosmological state in the form of a microcanonical density matrix has been proposed, which is an alternative to the known transcriptions of the tunneling wave function and the Hartle-Hawking wave function. The application of this concept to the model of multiple conformally invariant fields leads to a picture of the initial quasi-equilibrium thermal stage of the evolution of the Universe, preceding inflation and described by a cosmological instanton corresponding to the classically forbidden state of gravitational and material fields. This model opens up prospects for its unification with the theory of conformal higher spins, which will possibly solve the hierarchy problem between the scale of inflation and the Planck scale of quantum gravity.

Recent works by A. Barvinsky and co-authors include the study of local and non-local modifications of Einsteinian gravity (generalized unimodular theory of gravity, Horava-Lifshitz theory of gravity with broken Lorentz symmetry), aimed at constructing ultraviolet renormalizable quantum gravity and at solving the problem of the cosmological constant and dark energy.