Sunyaev and Yakov B. Zeldovich 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 Zeldovich 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. Zeldovich, at the Moscow Institute of Applied Mathematics, he proposed what is known as the Sunyaev-Zeldovich effect, which is due to electrons associated with gas in galaxy clusters scattering the cosmic microwave background radiation.