What does inflation really predict?

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If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Omegaₜot), dark energy (rhoₗambda, w, etc.), the primordial density fluctuations (Omegaₜot, dark energy (rhoₗambda, w, etc.). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and and the choice of measure underlying the calculation. We find that unless the characteristic scale Delta-phi on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions Omegaₜot 1+-0.00001, w=-1 and rhoₗambda in the observed ballpark but uncomfortably high. The high energy limit predicts nₛ 0.96, dnₛ/dlnk -0.0006, r 0.15 and nₜ -0.02, consistent with observational data and indistinguishable from eternal phi²-inflation. The low-energy limit predicts 5 parameters but prefers larger Q and redder nₛ than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favoring the detectable level r 0.03. (Abridged)