Galaxy Mergers in a Fractal Cosmology

This work discusses the influence of galaxy mergers in the evolution of a parabolic Lemaître-Tolman-Bondi (LTB) cosmology with simultaneous big bang endowed with two consecutive single fractal galaxy distributions systems possessing fractal dimension $D$. Based on recent empirical findings, it is assumed that the resulting galaxy mass from mergers can be expressed by a redshift dependent decaying power law. The proposed cosmological model modifies the relativistic fractal number counts distribution by including a merger rate evolution that estimates the model’s radial density. Numerical solutions for the first order small-merger-rate approximation (SMRA) are found and the results show that a fractal galaxy distribution having $D=1.5$ in the range $0.1<z<1.0$, and $D=0.5$ for $1<z<6$, as suggested by recent empirical findings, the SMRA allows consistent description of the model for a merger rate power law exponent up to $q=0.2$ considering a fractal galaxy distribution starting from the Local Group. Consistent values were also found up to $q=2.5$ and $z=7$ from a scale smaller than the Local Supercluster. These results show that galaxy mergers can be successfully incorporated into the dynamics of a parabolic LTB fractal cosmology.