00:01
We can plot the densities of different kinds of mass energy as a function of time, where dark energy has remained constant through the universe with the same overall density, while mass, that means dark matter or regular matter, have decreased by a factor of 1 over a cube, which is going to have a different relation to time.
00:45
In fact, it's going to be simpler to describe this with regards to the scale factor, which means that while in the current universe, mass is much, much weaker than the kind of, contributions from dark energy, there is going to have been some crossover point before which the attractive behavior of matter will have a stronger effect than the seeming repulsive effect of dark energy.
01:30
We can calculate when that will happen.
01:35
Matter density is proportional to one over r cubed.
01:45
So i can write r is proportional to one over density to the one -third.
01:55
And then write the statement r over r not is one over past density over current density to the one -third, or to make that simpler, row not over row final...