UDC 524.8 Fractal Properties of the Universe A. A. Agapov∗, I. K. Rozgacheva† ∗ Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, 117198, Russia † VINITI RAS 20, Usievicha str., Moscow, A-190, 125190, Russia Moscow State Pedagogical University, Moscow, Russia The large-scale structure of the Universe is revealed to be characterized by a range of powerlaws. <...> On basis of the hypothesis, the fractal cosmological model with scale invariant Lagrange’s field equation and Einstein’s equation permitting physical explanation of these properties is constructed. <...> The field energy densities (which are constant) and the space–time metrics of different domains differ in constant factors only. <...> Fractal properties of initial cosmological density perturbations remain and lead to presence of the fractal properties of the Universe’s large-scale structure which formed from them. <...> The nonsingular, compacted, pulsating and doubly-connected cosmological model as a partial solution for the homogeneous, isotropic and flat case is constructed. <...> A background radiation power spectrum has been computed. <...> The spectrum is shown to be close to the observable angular power spectrum of the SDSS-quasar distribution on the celestial sphere. <...> Key words and phrases: quasars, large-scale structure, fractal dimension, complex field, rotary symmetry, fractal properties of the large-scale structure, fractal cosmological model, background radiation. 1. <...> Introduction The large-scale structure of the Universe is the structure of the galaxy and quasar distribution in whole observable Universe’s volume. <...> The structure is sponge-like and composed of regions of a higher galaxy number density (filaments and planes of galaxies and galaxy clusters) bordering huge voids. <...> Investigation of geometrical properties of the large-scale structure of the Universe through galaxies, galaxy clusters, quasars and the CMB temperature anisotropy is an important area at present for understanding of galaxy and Universe evolution. <...> Estimation of distances to galaxies is complicated by low quality of spectra, by uncertainty of galaxy peculiar motion and by dependence on a cosmological model determining distance as a function of redshift. <...> The purposes of the present work are: – revealing of the fractal properties of the Universe’s large-scale structure; – construction of the fractal cosmological model permitting physical explanation of these properties; – the data processing on the quasar distribution on the celestial sphere <...>