Cosmology questions from a novice

Question

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.

Answer 1

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 $\rho=-p$.

As for your second question, the size of the black hole horizon is set by its mass. I don't see why this is logically problematic as you are implicitly suggesting.

Answer 2

The answer to question 1 is that astronomers assume the universe is spatially homogeneous and isotropic, meaning that it is roughly everywhere the same density, and the density only depends on time since the big-bang. this model is either true, or we are living at the only point in the universe where it appears to be true (since we can verify that it is true from our vantage point for concentric spheres around us, and it would require a conspiracy for these spheres to look like cross sections of a homogeneous universe if it weren't truly homogenous).

This assumption is justified theoretically today by inflationary cosmology, which predicts a homogeneous expansion with small corrections, which are predicted and matched. So it is both theoretically and observationally verified, and is certain in the scientific sense.

For the second question, you must remember than nothing can move faster than light, so if outgoing light is pulled inwards, matter, which must move slower, must be pulled inwards even more. This is why black holes can't be stablized matter which is compressed to a high density. But it isn't true that the matter is compressed to a single spatial point either, the interior is complicated, and the matter in a spherically symmetric collapse is compressed to a single point, but this point is a time, not a spatial position, because r and t switch inside a black hole. This is not easy to visualize outside of GR, using a Newtonian model, so all the usual popular pictures are misleading.