It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature. Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough pressure?
Or "magic" of cooking pasta is not in boiling and we would be able to cook pasta at 100°C without boiling water (at high pressure)?
No. Boiling itself doesn't mean that the water will cook anything. If you have boiling water at 30°C you could touch it (if we forget that it's at really low pressure) and nothing would happen. Boiling is not what cooks, but temperature.
In fact, if you want to purify water at high altitudes, you need to boil water for a longer time because it will be at a lower temperature.
Ahem, I come to you from Seasoned Advice (cooking). As @Beta suggested in a comment to the OP, questions like this one would not be uncommon there. The agitation of boiling water has nothing to do with cooking pasta except in that it helps keep the pasta from sticking.
Whether it makes good pasta to hydrate it without heat (or at least a lot of heat) is a source of some debate, but the pasta will be become hydrated (eventually) in even room temperature water, with or without a vacuum causing the water to boil.
Certainly the pasta would cook just fine, with no discernible difference in quality, if cooked (hydrated) in non-boiling 100C water (under pressure).
Well, I can share with you one experience from my high school. I wanted to boil coffee in my caffetier without a cooker. We had the vacuum pump in the physics room so there was the way to "boil" the water without getting it in 100°C. I did it... and coffee tasted horrible.
Never try it again.
Note that many of the other answers are assuming you are preparing dried pasta, which is of course by far the most common way of preparing pasta. Dried pasta is actually cooked (at temperatures between 60 and 70 degrees C) while it dries; fresh pasta (i.e. flour mixed with eggs and/or olive oil) does therefore need to be cooked in order for the gluten to polymerize correctly (see http://www.biw.kuleuven.be/m2s/clmt/lmcb/publications/docs/cbruneel for some more detail on the chemical processes that occur). It does not, however, need to boil. You should be able to cook it perfectly adequately at about 60 degrees, similarly to the way pasta is dried commercially.
If you hydrate pasta by keeping it in cold water, it won't be 'cooked' from a technical standpoint. Cooking requires heat (or the chemical equivalent, as in ceviche). It will taste like wet, raw flour.
Starches in the durum wheat flour will only activate at boiling temperature. Hydration is irrespective and can be achieved under vacuum.
