Vacuum energy: quantum hydrodynamics vs quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features, both have quadratic divergences, and both lead to the problem of the vacuum energy, which in the quantum gravity transforms to the cosmological constant problem. We show that in quantum liquids the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The vacuum energy is much smaller and is determined by the classical macroscopic parameters of the liquid including the radius of the liquid droplet. In the same manner the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant and the energy density of matter. The problem of quantum hydrodynamics is at least 65 years old (see quantization of the macroscopic dynamics of liquid in the first Landau paper on superfluidity of He [1]). It is almost as old as the problem of quantum gravity [2]. Quantum hydrodynamics and quantum gravity share many common features (e.g. both have quadratic divergences) and probably they will