cosmology - Why is the sky dark at night?

The question is the well-known Olbers' paradox:

If there are so many/infinite stars, in every direction, why is it dark at night? Where goes all the light we don't see?

Discussing with a friend we found different answers.

The first (my friend's answer) is that given the fact that in a finite amount of time (in this case, the age of the universe), light can travel only a certain, finite, distance, we cannot see, if they actually exist, stars farther than such distance (about 13 billions of years, I guess). Then he states (or better, I got him notice he implicitly does this) that within this radius there aren't enough stars to fill the night sky, and that's why we have darkness without sun's light.

The second answer (mine, or anyway the one I heard from a minutephysics YouTube video) is that despite of the big size of the observable universe, cosmological expansion red shifts most of the light out of the visible radiation range, so that the majority of light can't be seen by our eyes at night, while if we use, for example, an infrared camera, we should see a brighter sky, and lenghtening more and more the wavelength at which we observe the sky, we come to the uniform background radiation.

So my question is, what is the right answer? Is it one of the above-mentioned or even a third one?

EDIT: I've seen both answer may be acceptable, but what is the main contributing phenomenon?

Answer

I'm going to respond to (v1) of the question, which asks why the night sky is dark (black and unlit) compared to the day sky even though there are many light sources at night. The updated question references Olber's paradox, which has been answered many times before.

Like most things we see in everyday life, there are a number of reasons contributing to this. I'll go through each of the leading effects and what happens if we get rid of them.

First is my number one reason that the sky is dark at night simply because it doesn't require us to change the fundamental nature of the universe in order to imagine a universe without it. It is because most of the light from other stars is blocked by dust and gas clouds between us and the other stars.

Here's a picture:
_{(source: wikimedia.org)}

This is an image of the Milky Way as we see it from Earth. Without dust and gas, this would be so bright that the night sky would be lit up as well. This is mostly due to how bright the central bulge would be, but I'd be lying if I said the rest of the disk isn't bright as well. So most of the light that comes from other stars is blocked by dust and gas. Blocked of course meaning reflected, refracted away from us, or absorbed and retransmitted as invisible radiation.

Second, cosmological expansion. This gets the number two spot because of how important it is. The expansion of the universe causes light to be shifted to lower frequencies. The farther away it is, the more it is shifted. You have to change the nature of the universe to do it, but let's consider what it would be like without expansion: There's this thing called the Cosmic Microwave Background (CMB), which is background radiation that comes in almost equally from every direction. When it was produced, this radiation would have been as bright as if everywhere around you was the surface of a star (a reddish-orange star). Without expansion to redshift this to the microwave range, that's how bright the night sky would be now. That's significant right? Apparently not significant enough. Because of expansion, there is a cosmological event horizon, a distance at which things recede from us faster than light. Because of this, we can't see anything beyond that distance. So without expansion, all the stars and galaxies and light sources within our particle horizon but outside our event horizon would be visible (and not redshifted); so the night sky would be even brighter.

Third is the fact that the universe isn't infinite in age (technically we found that out because of the expansion of space, but this is my answer and I'll make it it's own thing if I want to). It has a finite age and that means light can only propagate a certain distance within that time. Therefore, we have a particle horizon, which means that there can only be a finite number of stars visible to us. This is great news because otherwise there would be an infinite number of stars visible to us and they would come in from every direction, which would make the sky as bright as the surface of the sun. That would be bad.

Those are the main three. Dust, expansion, and a finite age of the universe. You could say that expansion should be the frontrunner, but without expansion we really wouldn't be here and the universe would be fundamentally different. It's at least possible that our galaxy could have formed and given us a line-of-sight view to the galactic core, so dust and gas wins for actually keeping light from hitting us that could have in the first place.