  We analyze the necessary conditions for a body to remain rigid in an
expanding cosmological Universe. First, we establish the main theorems and
definitions for having a rigid body in a general spacetime as well as the new
concept of quasilocal rigidity. We apply the obtained results to a homogeneous
universe exploring the differences with flat spacetime. We discuss how the
concept of rigid body helps to understand the expansion of space in cosmology.
Finally, using a rigid system as a reference frame, we calculate the
gravitational energy, and we compare it with previous results in the
literature.
