We often say that QFT describes the nature on a fundamental level. However this is indeed a very complicated theory for which the calculations related to the interaction of just a few particles simply blow up.
So it is in principle an accurate and consistent theory but when applied in large scales e.g. large number of particles it will not be useful in practice to give us values about the variables such as energy.
Suppose we use the standard model of elementary particles to write the Hamiltonian or the Lagrangian density of the universe, then find the equation of motion, and compare the result of operating on the vacuum state with the standard model of cosmology.
In principle we write the Lagrangian involving strong and electroweak sections and the scalar section describing the curvature of spacetime. Now if we operate the Hamiltonian on the vacuum state of the universe we have the energy.
And then we can compare the result with the energy density of the universe obtained from the classical GR theory.
But given the huge number of the particles we can never compute the energy density of the whole universe in practice using QFT of all interacting fileds including gravity, strong, and electroweak and test the final value against the observation or the result from GR in cosmology.
So the questions are:
Am I correct in the above summary? If not which part is wrong?
If computations based on QFT are only possible for just a few number of particles then in what sense we say that the quantum theory is useful to describe the whole cosmos? It only describes the universe in principle but not in a practical useful and "falsifiable" sense.