The simplest inflationary model V = \frac { 1 } { 2 } m ^ { 2 } \phi ^ { 2 } represents the benchmark for future constraints .
For a quadratic potential , the quantity ( n _ { s } -1 ) + r / 4 + 11 ( n _ { s } -1 ) ^ { 2 } / 24 vanishes ( up to corrections which are cubic in slow roll ) and can be used to parametrize small deviations from the minimal scenario .
Future constraints on this quantity will be able to distinguish a quadratic potential from a pseudo-Nambu-Goldstone boson with f \lesssim 30 M _ { pl } and set limits on the deviation from unity of the speed of sound |c _ { s } -1 | \lesssim 3 \times 10 ^ { -2 } ( corresponding to an energy scale \Lambda \gtrsim 2 \times 10 ^ { 16 } \mathrm { GeV } ) , and on the contribution of a second field to perturbations ( \lesssim 6 \times 10 ^ { -2 } ) .
The limiting factor for these bounds will be the uncertainty on the spectral index .
The error on the number of e-folds will be \Delta N \simeq 0.4 , corresponding to an error on the reheating temperature \Delta T _ { \mathrm { rh } } / T _ { \mathrm { rh } } \simeq 1.2 .
We comment on the relevance of non-Gaussianity after BICEP2 results .