I have a question pertaining to the ideas behind the considered homogeneity and

Question

I have a question pertaining to the ideas behind the considered homogeneity and isotropic nature of the universe (at a grand scale) versus the theory of a chaotic and anisotropy structure of the universe. I am particularly ignorant on this subject, but I am assuming that the idea of fractal cosmology expresses that the universe has some sort of fractional pattern to it, which is the nature of fractal construct, and implies homogeneity. The Chaos Theory, which is tied to fractal pattern indicates that even the movement of chaos has a significant pattern. If so, wouldn't Misner's chaotic cosmology theory also result in a level homogeneity? If not, I would appreciate if someone could explain why or where I've made the wrong assumptions.

Thank you

Explanation / Answer

I am assuming that the idea of fractal cosmology expresses that the universe has some sort of fractional pattern to it, which is the nature of fractal construct, and implies homogeneity.

No, this is basically wrong. Homogeneity is mutually exclusive with fractal. This isn't my area either, but I will try to describe the state of our understanding based on the media I've consumed.

Fractal means that galaxies cluster on "ever larger scales". That would mean the universe isn't homogenous on any scale, and that the universe has similar matter distributions on repeated on different scales - essentially the definition of a fractal. This position has been argued by astronomers in recent memory.

People have done research into this exact question. Practically, you can randomly draw circles and then count the amount of matter within those circles. Then you can run statistics on the distribution of mass contained in those circles. If it is homogenous on the scale of the circles, then there will be little statistical deviation, but if it is not homogenous there will be a great deal. They did this exact thing and found that on very large scales there is basically no deviation from randomness. Thus, it was concluded that the universe is homogenous on large scale, and not fractal.

Everything I wrote is basically a summary of this video:

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