Fundamental cosmology based on unified theories of all the fundamental interactions (nuclear strong, nuclear weak, electromagnetic, and gravitational). Varying physical constants cosmologies. Observational and experimental consequences of the variability of physical constants. Superstring and M-theory cosmology. Brane cosmology. Pre-Big-Bang cosmology scenario and superinflation. Ekpyrotic/cyclic cosmology. Horava-Witten cosmology. The notions of the Multiverse and the superstring landscape. Inflation and large-scale structure of the universe. Large extra dimensions. Gravitational waves. Observational verification of the cosmological models (supernovae, baryon acoustic oscillations, cosmic microwave background, redshift drift). Phantom cosmology and phantom duality. Exotic singularity cosmologies (big-rip, sudden future singularities, finite scale factor singularities, big separation, w-singularities). Chaotic cosmology. Dark energy and quintessence. Quantum cosmology and loop quantum cosmology. The structure of space-time singularities. Inhomogeneous cosmology. Scalar-tensor cosmology. Conformally invariant cosmology.
Currently the group is running the project "New consequences of the variability of fundamental constants in physics and cosmology". It contains the problems related to the theoretical and observational consequences of timely and spatial variability of the speed of light c, gravitational constant G, fine structure constant α, proton to electron mass ratio and other physical constants. The scenarios of the evolution of the Universe with varying fundamental constants in the context of superstring theory (superstring landscape) and the Multiverse concept are also considered.