Sunyaev and Yakov B. Zel'dovich developed the theory for the evolution of density fluctuations in the early universe. They predicted the pattern of acoustic fluctuations that have been clearly seen by WMAP and other CMB experiments in the microwave sky and in the large-scale distribution of galaxies. Sunyaev and Zel'dovich stated in their 1970 paper, "A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations." CMB experiments have now seen this distinctive scale in temperature and polarization measurements. Large-scale structure observations have seen this scale in galaxy clustering measurements.
With Yakov B. Zel'dovich, at the Moscow Institute of Applied Mathematics, he proposed what is known as the Sunyaev-Zel'dovich effect, which is due to electrons associated with gas in galaxy clusters scattering the cosmic microwave background radiation.
Sunyaev and Nikolay I. Shakura developed a model of accretion onto black holes, from a disk, and he has proposed a signature for X-radiation from matter spiraling into a black hole. He has collaborated in important studies of the early universe, including the recombination of hydrogen and the formation of the cosmic microwave background radiation. He led the team which operated the X-ray observatory attached to the Kvant-1 module of the Mir space station and also the GRANAT orbiting X-ray observatory. Kvant made the first detection of X-rays from a supernova in 1987. His team is currently preparing the Spectrum-X-Gamma International Astrophysical Project and is working with INTEGRAL spacecraft data. At Garching he is working in the fields of theoretical high energy astrophysics and physical cosmology and participates in the data interpretation of the ESA Planck spacecraft mission.