Discrepancies between Observational Data and Theoretical Forecast in Single Field Slow Roll Inflation

Abstract

The PLANCK collaboration has determined values for the spectral parameters of the CMB radiation, namely the spectral index $n_s$, its running $\alpha_s$, the running of the running $\beta_s$, using a growing body of measurements of CMB anisotropies by the Planck satellite and other missions. These values do not follow the hierarchy of sizes predicted by single field, slow roll inflationary theory, and are thus difficult to fit for such inflation models. In this work we present first a study of 49 single field, slow roll inflationary potentials in which we assess the likelyhood of these models fitting the spectral parameters to their currently most accurate determination given by the PLANCK collaboration. We check numerically with a MATLAB program the spectral parameters that each model can yield for a very broad, comprehensive list of possible parameter and field values. The comparison of spectral parameter values supported by the models with their determinations by the PLANCK collaboration leads to the conclusion that the data provided by PLANCK2015 TT+lowP and PLANCK2015 TT,TE,EE+lowP taking into account the running of the running disfavours 40 of the 49 models with confidence level at least 92.8\%. Next, we discuss the reliability of the current computations of these spectral parameters. We identify a bias in the method of determination of the spectral parameters by least residue parameter fitting (using MCMC or any other scheme) currently used to reconstruct the power spectrum of scalar perturbations. This bias can explain the observed contradiction between theory and observations. Its removal is computationally costly, but necessary in order to compare the forecasts of single field, slow roll theories with observations.