How does mass affect the expansion of space?

Question

I'm a layman and I'm curious to understand how mass affects the expansion of space and whether the expansion of space is uniform everywhere in the universe.

From looking at redshifts it seems we have determined that until 5 billion years ago the expansion was slowing down and since then it has been speeding up. Supposedly the average density of mass in the universe is affecting the expansion - is this just conjecture and the only theory we have or is there some solid evidence for thinking this?

Wikipedia says "the scale of space itself changes" but that the model is valid only on large scales (galaxy clusters and above) and that the expansion cannot be observed on a smaller scale. wikipedia Is it possible that space between say, planet Earth and the Sun is actually expanding but is currently unobservable. If not, how far from our local group of galaxies do we have to look before we encounter some space that is actually expanding.

I realise that we don't understand what dark energy is and I much prefer answers that say "we don't know" if we really don't know.

I asked a question here and was unconvinced by the answers physics forum

Answer 1

The energy content of the space (i.e. radiation, normal matter, dark matter, and dark energy) determines the dynamics of the universe. AS you have mentioned, the universe is homogenous for large scales (>100 Mpc). It is only in this regime that we can use simple math models that apply to the whole universe and avoid doing simulations.

As I said before, the density of energy/matter determines the expansion rate. But expansion affects the density of different components of the universe differently. For instance, if you double the scale factor, the mass density shrinks by a factor of $2^3$ since matter is constant but space volume has octuple. In contrast, the energy density of dark energy remains the same. Freedman equation completely captures this dynamic:

$$\frac{(a'(t)/a(t))^2}{H_ 0^2}=\frac{\Omega _{\text{R0}}}{a(t)^4}+\frac{\Omega _{\text{M0}}}{a(t)^3}+\frac{\Omega _{\text{$\kappa $0}}}{a(t)^2}+\Omega _{\text{$\Lambda $0}}$$

where the Hubble constant $H_0 = 67.8 \frac{\text{km}/\text{s}}{\text{Mpc}} = 0.0693 /\text{Gyr}$, the present value of the radiation density $\Omega _{\text{R0}} = 0.0000905$, the present value of the matter density $\Omega _{\text{M0}} = 0.308$ (which mainly consist of dark matter) , the present value of the curvature density $\Omega _{\text{$\kappa $0}} = 1 - (\Omega _{\text{R0}} + \Omega _{\text{M0}} + \Omega _{\text{$\Lambda $0}}) = 1$, and the present value of the cosmological constant $\Omega _{\text{$\Lambda $0}} = 0.692$. These values are from the [Plank Collaboration 2015][1].