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The simplest inflationary model $V=\frac12 m^2\phi^2$ represents thebenchmark 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 inslow roll) and can be used to parametrize small deviations from the minimalscenario. Future constraints on this quantity will be able to distinguish aquadratic potential from a pseudo-Nambu-Goldstone boson with $f \lesssim 30M_{\rm pl}$ 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 asecond field to perturbations ($\lesssim 6 \times 10^{-2}$). The limitingfactor for these bounds will be the uncertainty on the spectral index. Theerror on the number of e-folds will be $\Delta N \simeq 0.4$, corresponding toan error on the reheating temperature $\Delta T_\mathrm{rh}/T_\mathrm{rh}\simeq1.2$. We comment on the relevance of non-Gaussianity after BICEP2 results.

$\phi^2$ or Not $\phi^2$: Testing the Simplest Inflationary Potential