Model-independent constraints on inflation and reheating
  Reheating connects the inflationary universe to the radiation-dominated
evolution of standard Big Bang cosmology. Due to the lack of direct
observations, we rely on indirect bounds on this phase from the Cosmic
Microwave Background (CMB) data. Using reheating constraints to arrive at
additional constraints on inflationary models is prevalent in the literature.
In this work, we develop a formalism to analyze the reheating constraints for
the general case of single field canonical slow-roll inflation without dealing
with a specific inflationary model. We find that using the lower bound on
reheating temperature and the upper bound on the tensor-to-scalar ratio: one
can constrain the inflationary energy scale and the duration of the reheating
epoch after slow-roll inflation. Following the standard practice, we described
the reheating phase with an effective equation of state parameter~($w_{\rm
re}$). However, with the present formalism, we can have quantitative
information of the reheating phase even when the reheating equation of state
behaves as radiation $w_{\rm re} = 1/3$. For the canonical reheating phase
described by $w_{\rm re}<1/3$, we find that the inflationary efolding number
must be bounded from above, i.e., $N_k\leq56.09$. Consequently, if inflationary
efolds satisfy this upper bound---i.e., $N_k=56.09$---a finite period of
reheating is only possible for exotic reheating phases described by $w_{\rm
re}>1/3$. We also find that as we lower the value of $N_k$, the corresponding
energy scale of inflation also decreases. Consequently, it will be more and
more difficult to detect the corresponding inflationary gravitational wave
signals with the Gravitational Waves mission. Finally, we show how an extended
period of canonical reheating can improve the situation in those cases.
