  The phenomenon of emergent physics in condensed-matter many-body systems has
become the paradigm of modern physics, and can probably also be applied to
high-energy physics and cosmology. This encouraging fact comes from the
universal properties of the ground state (the analog of the quantum vacuum) in
fermionic many-body systems, described in terms of the momentum-space topology.
In one of the two generic universality classes of fermionic quantum vacua the
gauge fields, chiral fermions, Lorentz invariance, gravity, relativistic spin,
and other features of the Standard Model gradually emerge at low energy. The
condensed-matter experience provides us with some criteria for selecting the
proper theories in particle physics and gravity, and even suggests specific
solutions to different fundamental problems. In particular, it provides us with
a plausible mechanism for the solution of the cosmological constant problem,
which I will discuss in some detail.
