# Why does the cosmological constant problem use the expectation value of the QFT vacuum energy?

As I understand it, the famous 120 orders of magnitude discrepancy between the observed cosmological constant and the calculated QFT vacuum energy density relies on the vacuum Einstein field equations

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \left< 0 |T_{\mu\nu}| 0 \right>.$$

The QFT vacuum energy expectation value $$\left<\rho_{vac}\right>$$ is formally infinite, but some natural cutoff is taken.

The quantum expectation value is the average value over many measurements. So why can we say that the vacuum is being measured? And if we can't say that there is wavefunction collapse, why should GR, a classical theory, care?

Of course this brings up the measurement problem. It is true that virtual particles can be realized, like for example in Hawking radiation, but this relies on some sort of wavefunction collapse due to interaction with the black hole. Since most of the universe is nearly empty, can we really say that vacuum fluctuations have an effect away from regions of appreciable matter and gravity?

For reference, I am coming at this from a mathematics background and the physics level of, say, a first graduate course in GR and QFT.