  It is believed that gravity will be explained in the framework of the
existing quantum theory when one succeeds in eliminating divergencies at large
momenta or small distances (although the phenomenon of gravity has been
observed only at nonrelativistic momenta and large distances). We consider a
quantum-mechanical description of systems of two free particles in de Sitter
invariant quantum theory (i.e. the paper contains nothing but the two-body de
Sitter kinematics). In our pure algebraic approach the cosmological constant
problem does not arise. It is shown that a system can be simultaneously
quasiclassical in relative momentum and energy only if the cosmological
constant is not anomalously small. We explicitly construct the relative
distance operator. The corresponding eigenvectors differ from standard ones at
both, large and small momenta. At large momenta they ensure fast convergence of
quasiclassical wave functions. There also exists an anomalously large (but
finite) contribution from small momenta, which is a consequence of the fact
that the cosmological constant is finite. We argue that gravity might be a
manifestation of this contribution.
