[Note: This was sent to several lists. Since the topic arises again and again, I've decided to place it here.]
<Define Olber's Paradox>
Olber's Paradox depends on several assumptions. If any of those assumptions fail, there's no paradoxical outcome.
I'd like to take an inventory of models that don't result in Olber's Paradox. Obviously, there are the finite models -- ones where space and time are finite. There are also various infinite models, including models where space is infinite but not time and vice versa. Then there are the IST (infinite space and infinite time) models. Even then, we could branch off into infinite vs. finite mass-energy...
Let me organize this better. The three basic parameters here are space, time, and mass-energy. This yields 8 model schemas:
1. finite space, finite time, finite mass-energy
2. finite space, infinite time, finite mass-energy
3. finite space, finite time, infinite mass-energy
4. finite space, infinite time, infinite mass-energy
5. infinite space, infinite time, infinite mass-energy
6. infinite space, infinite time, finite mass-energy
7. infinite space, finite time, infinite mass-energy
8. infinite space, finite time, finite mass-energy
Inside each of these, we can add in other features, such as global geometry and expansion rates. Regarding geometry, I can think of three global types: positive, zero, and negative curvature. Of course, things are more complex than that, even at the global level, but I don't know how much the complexities will affect the outcome. Obviously, type 5 models above that have zero global curvature are the most likely to fall prey to Olber's Paradox. Types 1, 2, 6, 7, and 8 would seem to escape it regardless of geometry -- though there might be a special case of each of these types that falls prey to it.
Focusing on just those types that allow for a non-special case escape from the paradox. 1, 2, 6, 7, and 8 would be those types. The Standard Model (of cosmology) is a type 1 model or a type 2 model if you allow for oscillation (i.e., expansions followed by contractions). In any of these models, Olber's Paradox need not arise, though we can probably safely ignore type 6, since that would imply, given dissipation, that the mass-energy density of the universe would be zero. (Even allowing for some sort of graininess for mass-energy, the chances of any two particles-- say a photon and an electron -- meeting were be infinitesimal. Since we do not see this, if type 6 is correct, then there must be some clumping process that accounts for what we see locally. Again, introducing this feels like adding Ptolemaic epicycles -- adding arbitrary hypotheses to save the theory from the data.)
Types 3 and 4 would seem to have special problems. Type 3 could escape having an infinite mass-energy density -- i.e., there could be local pockets of finite density -- because it would take time for the infinite mass-energy to spread out. That would place the observable universe in a very privileged position, which seems unlikely.
Type 4 doesn't even have that advantage, though one might argue that there would be local fluctuations in mass-energy density over infinite time spans. That, too, seems an arbitrary hypothesis.
This leaves us with the problem of type 5, which is the conventional way Olber's Paradox is read -- i.e., as refuting type 5. This is where I disagree. Certain types of type 5 models appear to avoid the paradox, such as those with high inflation or those with high negative curvature. (Don't the two go together? High inflation would seem to be a feature of a high negative curvature. [Is this correct?])
This is interesting because there's some observational support for negative curvature, BUT support for negative curvature is not necessarily support for any type 5 models. After all, a finite model can have negative curvature as well and account for the evidence.
I think we can also add into these models a maximum mass-energy density (before collapse, that is, though via Quantum Field Theory there does seem to be a case for an absolute maximum even after collapse) and mass-energy quantization..