Despite its importance for modeling the homogeneous hot early universe very little is experimentally known about the magnitude of the reheating temperature , leaving an uncertainty of remarkable 18 orders of magnitude .
In this paper we consider a general class of polynomial inflaton potentials up to fourth order .
Employing a Monte Carlo scan and imposing theoretical and experimental constraints we derive a robust lower limit on the energy scale at the end of inflation , V _ { \text { end } } ^ { 1 / 4 } > 3 \times 10 ^ { 15 } GeV for sizable tensor modes , r \geq 10 ^ { -3 } .
If the reheating phase is perturbative and matter dominated , this translates into a lower bound on the reheating temperature , yielding T _ { \text { rh } } > 3 \times 10 ^ { 8 } ( 7 \times 10 ^ { 2 } ) GeV for gravitational inflaton decay through a generic dimension five ( six ) operator .