  A nonvanishing cosmological term in Einstein's equations implies a
nonvanishing spacetime curvature even in absence of any kind of matter. It
would, in consequence, affect many of the underlying kinematic tenets of
physical theory. The usual commutative spacetime translations of the Poincare'
group would be replaced by the mixed conformal translations of the de Sitter
group, leading to obvious alterations in elementary concepts such as time,
energy and momentum. Although negligible at small scales, such modifications
may come to have important consequences both in the large and for the
inflationary picture of the early Universe. A qualitative discussion is
presented which suggests deep changes in Hamiltonian, Quantum and Statistical
Mechanics. In the primeval universe as described by the standard cosmological
model, in particular, the equations of state of the matter sources could be
quite different from those usually introduced.
