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 $zeta eq {cal R}$. 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.
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