  We address the question whether a medium featuring $p + \rho = 0$, dubbed
$\Lambda$- medium, has to be necessarily a cosmological constant. By using
effective field theory, we show that this is not the case for a class of media
comprising perfect fluids, solids and special super solids, providing an
explicit construction. The low energy excitations are non trivial and lensing,
the growth of large scale structures can be used to clearly distinguish
$\Lambda$-media from a cosmological constant.
