It is well known that the inflationary scenario often displays different sets of degeneracies in its predictions for CMB observables. These degeneracies usually arise either because multiple inflationary models predict similar values for the scalar spectral index $n_{_S}$ and the tensor-to-scalar ratio $r$, or because within the same model, the values of $lbrace n_{_S}, r rbrace$ are insensitive to some of the model parameters, making it difficult for CMB observations alone to constitute a unique probe of inflationary cosmology. We demonstrate that by taking into account constraints on the post-inflationary reheating parameters such as the duration of reheating $N_{_{rm re}}$, its temperature $T_{_{rm re}}$ and especially its equation of state (EOS), $w_{_{rm re}}$, it is possible to break this degeneracy in certain classes of inflationary models where identical values of $lbrace n_{_S}, r rbrace$ can correspond to different reheating $w_{_{rm re}}$. In particular, we show how reheating constraints can break inflationary degeneracies in the T-model and the E-model $alpha$-attractors. Non-canonical inflation is also studied. The relic gravitational wave (GW) spectrum provides us with another tool to break inflationary degeneracies. This is because the GW spectrum is sensitive to the post-inflationary EOS of the universe. Indeed a stiff EOS during reheating $(w_{_{rm re}} > 1/3)$ gives rise to a small scale blue tilt in the spectral index $n_{_{rm GW}} = frac{dlog{Omega_{_{rm GW}}}}{dlog{k}} > 0$, while a soft EOS $(w_{_{rm re}} < 1/3)$ results in a red tilt. Relic GWs therefore provide us with valuable information about the post-inflationary epoch, and their spectrum can be used to cure inflationary degeneracies in $lbrace n_{_S}, rrbrace$.
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