  We present some new ideas on how to design analogue models of quantum fields
living in curved spacetimes using ultra-cold atoms in optical lattices. We
discuss various types of static and dynamical curved spacetimes achievable by
simple manipulations of the optical setup. Examples presented here contain
two-dimensional spaces of positive and negative curvature as well as
homogeneous cosmological models and metric waves. Most of them are extendable
to three spatial dimensions. We mention some interesting phenomena of quantum
field theory in curved spacetimes which might be simulated in such optical
lattices loaded with bosonic or fermionic ultra-cold atoms. We also argue that
methods of differential geometry can be used, as an alternative mathematical
approach, for dealing with realistic inhomogeneous optical lattices.
