UDC 524.8:530.191 The Anisotropy Properties of a Background Radiation in the Fractal Cosmological Model 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 We consider the anisotropy properties of a background radiation in the fractal cosmological model. <...> The metric tensors of any two domains are connected by the discrete scaling transformation. <...> Photons of the background radiation cross the domain and their energies change. <...> Any observer receives these photons from different domains and detects spots with different brightness. <...> The power spectrum of the brightness anisotropy of the background radiation in the fractal cosmological model is calculated. <...> It is shown this spectrum is closed to the observed angular power spectrum of the SDSS-quasar distribution on the celestial sphere. <...> Only qualitatively it conforms to the angular power spectrum of CMB (WMAP-7). <...> Key words and phrases: complex field, rotary symmetry, fractal properties of the large-scale structure, fractal cosmological model, background radiation. 1. <...> We adduce here some power-laws indicating the fractality. – The correlation dimension characterizes galaxy clumping degree and difference of the galaxy distribution from a homogenous and isotropic one. <...> For example, the dependence of a SDSS-quasar number N (r) in a sphere on its radius r is described by a power-law [3]: We call the fractal properties of the large-scale galaxy distribution and the CMB N ( r) ∼ rdc , – The angular correlation function ω (ϑ) and the angular power spectrum ul of the SDSS-quasar distribution approximate to power-laws at the average [3]: where the exponent is the correlation dimension, it equals dc ≈ 2.17. ω (ϑ) ∼ ϑ−1.08, ul ∼ l−1.08, (2) (3) – Large-scale quasar clumps are discovered in the SDSS-quasar distribution. <...> The relation between a number of clumps N (ϑc) and their angular size ϑc is characterized by a power-law [3]: Nc ∼ ϑc−2.02. <...> The authors thank the FCPK grant 16.740.11.0465 for support of the work. (4) – The angular power spectrum of the CMB temperature fluctuations according to WMAP-7 data approximates to a power-law at the average [3]: (5) where l is a multipole moment number in expansion of the quasar distribution <...>