  Bayesian model comparison penalizes models with more free parameters that are
allowed to vary over a wide range, and thus offers the most robust method to
decide whether some given data require new parameters. In this paper, we ask a
simple question: do current cosmological data require extensions of the
simplest single-field inflation models? Specifically, we calculate the Bayesian
evidence of a totally anti-correlated isocurvature perturbation and a running
spectral index of the scalar curvature perturbation. These parameters are
motivated by recent claims that the observed temperature anisotropy of the
cosmic microwave background on large angular scales is too low to be compatible
with the simplest inflation models. Both a subdominant, anti-correlated cold
dark matter isocurvature component and a negative running index succeed in
lowering the large-scale temperature power spectrum. We show that the
introduction of isocurvature perturbations is disfavored, whereas that of the
running spectral index is only moderately favored, even when the BICEP2 data
are included in the analysis without any foreground subtraction.
