  From a model-building perspective, the inflationary sector might very well
have no direct couplings to other species, apart from inevitable gravitational
interactions. Within the context of General Relativity, a thermal universe can
still emerge after inflation if: $i)$ some radiation sector is excited towards
the end of inflation, and $ii)$ the post-inflationary equation of state becomes
sufficiently stiff $w \geq w_{\rm RD}\gtrsim 0.57$, with $w_{\rm RD}$ a
threshold depending on the inflationary scale $H_*$ and the initial
radiation-to-inflaton energy ratio $\Delta_*$. Furthermore, a stiff period in
the expansion history enhances significantly the inflationary gravitational
wave (GW) background, making this signal (potentially) observable by aLIGO,
LISA and other experiments. The very same enhancement leads however to an
inconsistency of the scenario: the energy of the GWs becomes too large compared
to the rest of the radiation sector, violating standard BBN and CMB bounds on
GW backgrounds. Except for very special scenarios where the initial radiation
sector comprises hundreds of fields with couplings tuned to specific values,
our result applies independently of $w$, $H_*$ and $\Delta_*$. This suggests
that in order to reheat the universe, the inflationary sector should be coupled
directly to other particle species. Alternatively the inflationary sector could
be implemented in modified gravity theories.
