Precision of inflaton potential reconstruction from CMB using the general slow-roll approximation

Through a principal component analysis, we study how accurately cosmic microwave background observables can constrain inflaton potentials in a model-independent manner. We apply the general slow-roll approximation in our analysis where we allow, in contrast to the standard slow-roll approximation, the possibility of variations in V''(phi) and take into account the fact that horizon crossing is not an instantaneous event. Our analysis provides a set of modes to be used in fitting observables. We find that of order five of these modes will be constrained by future observations, so a fully general data analysis package could use the amplitudes of just a handful of modes as free parameters and retain all relevant information in the data.