Violation of the Pauli principle and dimension of the Universe at very large distances

We discuss a Modified Field theory (MOFT) in which the number of fields can vary. It is shown that in MOFT fermions obey the so-called parastatistics in which the order of the parastatistics depends on scales. In particular, at very large distances $r>r_{\min }$ fermions violate the Pauli principle. It is also shown that in MOFT in some range of scales $r_{\max }>r>r_{\min }$ the Universe acquires features of a two-dimensional space whose distribution in the observed 3-dimensional volume has an irregular character. This provides a natural explanation to the observed fractal distribution of galaxies and the logarithmic behavior of the Newton’s potential for a point source.