The condensed matter analogs are useful for consideration of the phenomena related to the quantum vacuum. This is because in condensed matter we know physics both in the infrared and in the ultraviolet limits, while in particle physics and gravity the physics at trans-Planckian scale is unknown. One of the corner stones of the connections between the non-relativistic condensed matter and the modern relativistic theories is the two-fluid hydrodynamics of superfluid helium, which was developed by Landau and Khalatnikov (Isaak Markovich Khalatnikov later founded and headed the Landau Institute). The dynamics and thermodynamics of the de Sitter state of the expansion of the Universe bear some features of the multi-fluid system. There are actually three components: the quantum vacuum, the gravitational component and relativistic matter. The expanding de Sitter vacuum serves as the thermal bath with local temperature, which is twice the Gibbons-Hawking temperature related to the cosmological horizon. This local temperature leads to the heating of matter component and the gravitational component. The latter behaves as Zel'dovich stiff matter and represents the dark matter. In equilibrium and in the absence of the conventional matter the positive partial pressure of dark matter compensates the negative partial pressure of quantum vacuum. That is why in the full equilibrium the total pressure is zero. This is rather similar to the correspondingly superfluid and normal components of superfluid liquid, which together produce the zero pressure of the liquid in the absence of environment. We suggest the phenomenological theory, which describes the dynamics of the dark energy and the dark matter. If one assumes that in dynamics, the gravitational dark matter behaves as the real Zel’dovich stiff matter, one obtains that both components experience the power law decay due to the energy exchange between these components. Then it follows that their values at present time have the correct order of magnitude. We also consider the other problems through the prism of condensed matter physics, including the black holes and Planck constant.