Cosmology questions from a novice

These ideas/questions probably represent a lack of understanding on my part, but here they are:

1) Cosmologists talk about the increasing speed of expansion of the universe and talk of dark energy as the cause. But, I keep thinking that the farther out we observe, is farther back in time and the light we observe is from a time billions of years ago. We don't know what they look like or how fast they are moving now. Who's to say they haven't slowed down? How can we know now? So, how can we say that the universe is increasing in it's rate of expansion? All we can say for sure is that it was expanding at that rate.

Another thought- on black holes:

2) If Black holes where not composed of highly dense matter, why would there be different "sizes" of Black holes. if all black holes were collapsed to a "singularity", there should be no difference in "size" (the diameter of the light free area). Therefore, I have trouble with the singularity concept and think they are just another form of dense matter that just happens to have enough gravity to hold back even photons.

• The difference in "size" of a black hole is not a difference in the singularity but in the event horizon where general relativistic physics is still well behaved. – dmckee Dec 1 '12 at 3:19
• This wiki article might help your understanding en.wikipedia.org/wiki/Expanding_universe . The short answer to your first questions is "the theory fits the data we observe", mathematial extrapolations give us the other perspectives. – anna v Dec 1 '12 at 5:03

The universe is accelerating in the sense that you fit the data (e.g. from very far away supernovae of a certain type) better by taking $\ddot{a}>0$ than otherwise. $a(t)$ is the scale factor in FLRW metric, e.g. $ds^2=a^2(t)(-dt^2+d\vec{x}^2)$. From Friedman equation you get that $\rho+3p<0$ which requires a very special type of matter, generically dubbed dark energy. A cosmological constant is one important example with $\rho=-p$.