  We study the dynamics of inflation driven by an adiabatic self-gravitating
medium, extending the previous works on fluid and solid inflation. Such a class
of media comprises perfect fluids, zero and finite temperature solids. By using
an effective field theory description, we compute the power spectrum for the
scalar curvature perturbation of constant energy density hypersurface $\zeta$
and the comoving scalar curvature perturbation ${\cal R}$ in the case of
slow-roll, super slow-roll and $w$-media inflation, an inflationary phase with
$w$ constant in the range $-1 <w <-1/3$. A similar computation is done for the
tensor modes. Adiabatic media are characterized by intrinsic entropy
perturbations that can give a significant contribution to the power spectrum
and can be used to generate the required seed for primordial black holes. For
such a media, the Weinberg theorem is typically violated and on super horizon
scales neither $\zeta$ nor ${\cal R}$ are conserved and moreover $\zeta \neq
{\cal R}$. Reheating becomes crucial to predict the spectrum of the imprinted
primordial perturbations. We study how the difference between $\zeta$ and
${\cal R}$ during inflation gives rise to relative entropic perturbations in
$\Lambda$CDM.
