I have a question about the expansion of the universe and the 1st law of thermodynamics.

Answer

This question has been answered before on this site – in a slightly different form. But no problem doing it again, because it’s an important question. If there is a fundamental law in physics, it is certainly conservation of energy; a theory that does not meet this requirement is worthless. Incidentally, the two most famous equations in physics – Einstein’s on gravitation and the Schrodinger equation in quantum physics – primarily express energy conservation.

The expansion of the universe is the solution of Einstein’s equation: it must therefore satisfy energy conservation. And that is also the case. In the first law (dE = dU + P dV), the term P dV is that of the work done. The volume V increases, but to do work there must also be pressure (P). The two components that contribute to the energy of the universe (matter and radiation; let’s leave out ‘dark energy’) behave differently here. Matter hardly exerts any pressure (galaxies collide so much less often than molecules in a gas) and thus do no work; conservation of energy for matter simply means that density decreases inversely proportional to the cube of the size of the universe. The radiation (which we observe in the cosmological background radiation) DOES exert pressure, and therefore work. And that is precisely why its temperature does decrease with cosmic time. We can determine this experimentally, by the way: today its temperature is about 3 degrees above absolute zero, but there are indications that this temperature for distant galaxies – which we see in an earlier phase – was indeed higher, exactly according to what its theory says. . Furthermore, several important data about the early universe are only correct if the temperature was indeed higher according to the application of the first law.