Single field inflationary models with a nonminimal kinetic term (also called $k$-inflationary models) can be characterized by the so-called sound flow functions, which complete the usual Hubble flow hierarchy. These parameters appear in the primordial power spectra of cosmological perturbations at leading order and, therefore, affect the resulting cosmic microwave background anisotropies. Using the fifth year Wilkinson Microwave Anisotropy Probe (WMAP5) data, we derive the marginalized posterior probability distributions for both the sound and Hubble flow parameters. In contrast to the standard situation, these parameters remain separately unbounded, and notably there is no longer any upper limit on ${ϵ}_1$, the first Hubble flow function. Only special combinations of these parameters, corresponding to the spectral index and tensor-to-scalar ratio observables, are actually constrained by the data. The energy scale of $k$-inflation is nevertheless limited from above to $H_{\inf }\le 6\times {10}^{-6}{m}_{\mathrm{Pl}}$ at two-sigma level. Moreover, for the subclass of Dirac-Born-Infeld models, by considering the non-Gaussianity bounds on the sound speed, we find a weak limit ${ϵ}_1<0.08$ at 95% confidence level.

• Received 16 July 2008

DOI:https://doi.org/10.1103/PhysRevD.78.063543