The first law of thermodynamics states that [tex]dU = -PdV + dQ[/tex](adsbygoogle = window.adsbygoogle || []).push({});

We can apply this to the expansion of the universe by assuming the expansion of space is a adiabatic process, i.e. [itex]dQ = 0[/itex]. Together with the FW metric, we end up with one of the Friedman Equations: [tex]\dot{\rho} = -\frac{3\dot{a}}{a}(p + P/c^{2})[/tex]

Now let's focus on a cubic region of space. In the case P=0, this means that [itex]\dot{\rho} = -\frac{3\dot{a}}{a}(p)[/itex]. This makes sense because this accounts for the fact that when the universe expands, the energy density within get diluted. However, when P != 0, we also have the term [itex]-\frac{3\dot{a}}{a}(P/c^{2})[/itex]. This terms correspond to the [itex]-pdV[/itex] term in the thermodynamics equation. In other words, the energy in the region decreases not just because of dilution, but also because part of the energy is used to "push" the matter outside the region.

My question is, where has the energy that used to "push" the matter outside the region gone? Obviously energy has to be conserved. So the lost energy must have gone to somewhere.

Thanks!

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# Conservation of Energy in Friedman Equation

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