Question about dark matter gravity and the expanding universe.

[Tanelorn]

ok thanks Ben, this had been gnawing at the back of my mind since the properties of space thread, probably still is..

 

[bapowell]

However, two questions remain unsolved for me.

I think much of your confusion stems for your attempt to understand cosmology and gravitation in general using the laws of Newton. The example I showed above is a Newtonian approximation that only makes sense in the case of weak gravitational fields; after all, GR indeed reduces to Newtonian gravity in this limit. However, more generally one must apply GR in order to understand the gravitational dynamics of the universe at large.

1. Why do we regard the gravitational attraction and the cosmological repulsion as aspects of one and the same force (field)? Or, to put it otherwise, would it be alright if I would say that there is a fundamental force called gravitation that is always attracting, proportional to mass and inversely proportional to distance squared, and that there is another fundamental force called the cosmological force that is always repulsive and proportional to the distance? If not, then why not add the formula for electrical attraction and repulsion (and those for strong and weak forces) as well to this sum?

This expression determines the acceleration due to gravity that arises from two distinct stress-energy ingredients: ordinary matter and a cosmological constant, again, with the caveat that one is working in the weak field limit. The gravitational properties of the two components are opposite -- one attractive and the other repulsive.

2. What does it mean that the universe consists of 27% (light and dark) matter and 73% vacuum energy? From the formula, a comparison between the two terms only makes sense if a particular value of r is chosen. And the only reasonable value I can think of to choose would be the radius of the visible universe. But still, how do we know these proportions? We can measure (very unaccurately) the acceleration in the distant universe and derive a value for lambda from there. And we might estimate all gravitating matter by observing the dynamics of clusters etc. Is this the way this calculation is done? I can't imagine we can acquire an accurate result from this.

It is not appropriate to apply this formula to the large scale evolution of the universe, and it is only on these large scales that the decomposition of the universe into matter and dark energy is relevant. This decomposition is best understood by examining the properties of the cosmic microwave background within the context of the isotropic and homogeneous Friedmann cosmology.