RECONSTRUCTING THE INFLATON POTENTIAL - PERTURBATIVE RECONSTRUCTION TO 2ND-ORDER

One method to reconstruct the scalar field potential of inflation is a perturbative approach, where the values of the potential and its deri vatives are calculated as an expansion in departures from the slow-rol l approximation. They can then be expressed in terms of observable qua ntities, such as the square of the ratio of the gravitational wave amp litude to the density perturbation amplitude, the deviation of the spe ctral index from the Harrison-Zel'dovich value, etc. Here, we calculat e complete expressions for the second-order contributions to the coeff icients of the expansion by including for the first time corrections t o the standard expressions for the perturbation spectra. As well as of fering an improved result, these corrections indicate the expected acc uracy of the reconstruction. Typically the corrections are only a few percent.