Galaxy mergers in a fractal cosmology

Abstract 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 $$D=1.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math> in the range $$0.1&lt;z&lt;1.0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.1</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>z</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:math> , and $$D=0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> for $$1&lt;z&lt;6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>z</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> , as suggested by recent empirical findings, the SMRA allows consistent description of the model for a merger rate power law exponent up to $$q=0.2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> </mml:math> considering a fractal galaxy distribution starting from the Local Group. Consistent values were also found up to $$q=2.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math> and $$z=7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> 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.