Density contrast inside a region at turnaround.

[akr6]

Hello everyone,

I have a question that I was not able to find (and think of) an intuitive answer.

It is well known that density perturbations in the early universe grows with time such that some eventually form the non-linear objects that are stars and galaxies. One can follow a spherical region with enclosed mass M and determine the time and size at which it eventually decouples from the Hubble flow. Solving the equation in parametric form allows us to determine that the average density inside that sphere which now starts to collapse is 5.5 times bigger than the background density (given by the critical density of the universe).

Now this ends up being true with no dependence on the original mass M enclosed in the sphere. What I don't understand is: if I choose an initial M to be such that the average density in the sphere is bigger than 5.5 times the critical density, by the time its expanding outermost shell turnaround the sphere would enclose an average density bigger than what is predicted. Where is the flaw in my reasoning? And why is the turnaround over-density contrast independent of the initial enclosed mass and density?

Thank you

 

[AndyW]

for your question. The key concept to understand here is the concept of critical density. Critical density is the density at which the expansion of the universe is balanced by the gravitational pull of matter, resulting in a flat universe. In the early universe, density perturbations grow due to gravitational attraction, but the overall expansion of the universe also affects their growth.

In your scenario, even if the initial mass enclosed in the sphere is larger than the critical density, the expansion of the universe will still have an effect on the growth of the density perturbations. This means that the density inside the sphere will not continue to increase indefinitely, but will eventually reach a maximum value before collapsing. This maximum value is 5.5 times the critical density, which is why the turnaround over-density contrast is independent of the initial enclosed mass and density.

In other words, the overall expansion of the universe acts as a limiting factor on the growth of density perturbations, preventing them from exceeding a certain threshold. This is a fundamental principle in understanding the formation of structures in the early universe.

I hope this helps clarify your question. If you have any further questions, please don't hesitate to ask.