Is our universe getting colder due to expansion?

Answer

Conservation of energy is a basic law of physics. No physical theory that does not conform to it can be correct. By the way, the equations describing the expanding universe are based on energy conservation.

In thermodynamics, energy conservation is expressed in the so-called ‘first law’ as dE = dU + P dV = 0.

Here the symbols mean the following: E ​​is the total energy, U is the internal energy, P is the pressure, V is the volume; the d’s stand for ‘change of’ (differential). That term ‘P dV’ is therefore the product of the pressure P and the change dV of the volume V, which is called ‘work’.

So the first law states that the change of the internal energy plus the work done gives zero.

Several cases can be distinguished:

1) The component ‘matter’ in the universe. The universe is represented as a gas of galaxies. These interact little with each other, they exchange little movement, so the pressure is zero. The total internal energy U must therefore be constant (dU = 0). The total internal energy is equal to the energy per unit volume (energy density) times the volume: U = u V. Since the volume V increases with the expansion, the energy density must decrease: u decreases by 1 divided by the cube of the ‘radius’ R. Indeed, if the dimensions increase by a factor of 2, the volumes increase by a factor of 8, and the mass per unit volume is 8 times smaller.

2) The component ‘radiation’ in the universe. Radiation does exert pressure, so there is a term of labor. It is eventually found that the energy density of radiation decreases according to 1 divided by the fourth power of the ‘radius’ R. This is where the effect you mean occurs. The radiation of the universe cools, and the individual photons (radiation particles) lose energy due to the work they do. The temperature continues to fall, and after an infinite time it becomes zero.

3) And now the ‘dark energy’. Which gives you a constant energy density to the empty space. The total internal energy U = uV in the dark energy thus increases with the expansion. Energy conservation is then given by dE = (u + P) dV = 0. This is only possible if u + P = 0. The energy of the empty space is positive (this is what the observations teach us), so the dark energy must be given a negative pressure associated! The expansion of the empty space of the universe thus produces negative work. In other words, work is done on empty space through expansion. Strange but true.