Is a step in the primordial spectral index favoured by CMB data?

Abstract

A sudden small change in the second derivative of the inflaton potential can result in a universal local feature in the spectrum of primordial perturbations generated during inflation. The exact solution describing this feature is characterized by a step in the spectral index modulated by characteristic oscillations and results in a large running of the spectral index localized over a few e-folds of scale. In this paper we confront this step-like feature with the 5 year WMAP results and demonstrate that it provides a better fit to this data than a featureless initial spectrum. If such a feature exists at all, then it should lie at sufficiently large scales k₀ ≳ 0.003 Mpc⁻¹ corresponding to l ≳ 40. The sign of the effect is shown to correspond to the negative running of ns localized near this scale. This feature could arise as a result of a 'mini-waterfall'-type fast second order phase transition experienced by an auxiliary heavy field during inflation, in a model similar to hybrid inflation (though for a different choice of parameters). If this is the case, then the auxiliary field should be positively coupled to the inflaton.