φ2 or Not φ2: Testing the Simplest Inflationary Potential

The simplest inflationary model V = 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 less than or similar to 30M(pl) and set limits on the deviation from unity of the speed of sound |C-s - 1| less than or similar to 3 x 10(-2) (corresponding to an energy scale Lambda greater than or similar to 2 x 10(16) GeV) and on the contribution of a second field to perturbations (less than or similar to 6 x 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 similar or equal to 0.4, corresponding to an error on the reheating temperature Delta T-rh/T-rh similar or equal to 1.2. We comment on the relevance of non-Gaussianity after BICEP2 results.