A model-independent fit to Planck and BICEP2 data

Inflation is the leading theory to describe elegantly the initial conditions that led to structure formation in our universe. In this paper, we present a novel phenomenological fit to the Planck, WMAP polarisation (WP) and the BICEP2 datasets using an alternative parameterisation. Instead of starting from inflationary potentials and computing the inflationary observables, we use a phenomenological parameterisation due to Mukhanov, describing inflation by an effective equation-of-state, in terms of the number of e-folds and two phenomenological parameters $\alpha$ and $\beta$. Within such a parametrisation, which captures the different inflationary models in a model-independent way, the values of the scalar spectral index $n_s$, its running and the tensor-to-scalar ratio $r$ are predicted, given a set of parameters $(\alpha,\beta)$. We perform a Markov Chain Monte Carlo analysis of these parameters, and we show that the combined analysis of Planck and WP data favours the Starobinsky and Higgs inflation scenarios. Assuming that the BICEP2 signal is not entirely due to foregrounds, the addition of this last data set prefers instead the $\phi^2$ chaotic models. The constraint we get from Planck and WP data alone on the derived tensor-to-scalar ratio is $r<0.18$ at $95\%$~CL, value which is consistent with the one quoted from the BICEP2 collaboration analysis, $r = 0.16^{+0-06}_{-0.05}$, after foreground subtraction. This is not necessarily at odds with the $2\sigma$ tension found between Planck and BICEP2 measurements when analysing data in terms of the usual $n_s$ and $r$ parameters, given that the parameterisation used here includes, implicitly, a running spectral index.