The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson matter field (complex field). They may be explained through a conception of the Universe as an assembly of self-similar space-time domains. We have found the scale invariant solutions of Einstein's equation and Lagrange's field equation. For the solution the space-time domains with field values related by the scaling are geometrically similar and evolve similarly. Due to this, fractal properties of initial density perturbations which lead to formation of the large-scale structure remain during the gravitational evolution and lead to presence of the fractal properties in the large-scale structure
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