Brane inflation and the WMAP data: a Bayesian analysis

The Wilkinson Microwave Anisotropy Probe (WMAP) constraints on string inspired 'brane inflation' are investigated. Here, the inflaton field is interpreted as the distance between two branes placed in a flux-enriched background geometry and has a Dirac–Born–Infeld (DBI) kinetic term. Our method relies on an exact numerical integration of the inflationary power spectra coupled to a Markov chain Monte Carlo exploration of the parameter space. This analysis is valid for any perturbative value of the string coupling constant and of the string length, and includes a phenomenological modelling of the reheating era to describe the post-inflationary evolution. It is found that the data favour a scenario where inflation stops by violation of the slow-roll conditions well before brane annihilation, rather than by tachyonic instability. As regards the background geometry, it is established that logv>−10 at 95% confidence level (CL), where v is the dimensionless ratio of the five-dimensional sub-manifold at the base of the six-dimensional warped conifold geometry to the volume of the unit 5-sphere. The reheating energy scale remains poorly constrained, Treh>20 GeV at 95% CL, for an extreme equation of state (w_{\mathrm {reh}} \gtrsim-1/3 ) only. Assuming that the string length is known, the favoured values of the string coupling and of the Ramond–Ramond total background charge appear to be correlated. Finally, the stochastic regime (without and with volume effects) is studied using a perturbative treatment of the Langevin equation. The validity of such an approximate scheme is discussed and shown to be too limited for a full characterization of the quantum effects.