Evidence from the BICEP2 experiment for a significant gravitational-wave background has focussed attention on inflaton potentials V ( \phi ) \propto \phi ^ { \alpha } with \alpha = 2 ( “ chaotic ” or “ m ^ { 2 } \phi ^ { 2 } ” inflation ) or with smaller values of \alpha , as may arise in axion-monodromy models .
Here we show that reheating considerations may provide additional constraints to these models .
The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter w _ { re } .
The canonical reheating scenario is then described by w _ { re } = 0 .
The simplest \alpha = 2 models are consistent with w _ { re } = 0 for values of n _ { s } well within the current 1 \sigma range .
Models with \alpha = 1 or \alpha = 2 / 3 require a more exotic reheating phase , with -1 / 3 < w _ { re } < 0 , unless n _ { s } falls above the current 1 \sigma range .
Likewise , models with \alpha = 4 require a physically implausible w _ { re } > 1 / 3 , unless n _ { s } is close to the lower limit of the 2 \sigma range .
For m ^ { 2 } \phi ^ { 2 } inflation and canonical reheating as a benchmark , we derive a relation \log _ { 10 } \left ( T _ { re } / 10 ^ { 6 } { GeV } \right ) \simeq 2000 ( n _ { s } -0.96 ) between the reheat temperature T _ { re } and the scalar spectral index n _ { s } .
Thus , if n _ { s } is close to its central value , then T _ { re } \lesssim 10 ^ { 6 } GeV , just above the electroweak scale .
If the reheat temperature is higher , as many theorists may prefer , then the scalar spectral index should be closer to n _ { s } \simeq 0.965 ( at the pivot scale k = 0.05 { Mpc } ^ { -1 } ) , near the upper limit of the 1 \sigma error range .
Improved precision in the measurement of n _ { s } should allow m ^ { 2 } \phi ^ { 2 } , axion-monodromy , and \phi ^ { 4 } models to be distinguished , even without precise measurement of r , and to test the m ^ { 2 } \phi ^ { 2 } expectation of n _ { s } \simeq 0.965 .