Primordial Fluctuations and Non-Gaussianities in Multifield Dirac-Born-Infeld Inflation

Abstract

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case. The past decade has seen an accumulation of cosmological data of increasing precision. Together with future experiments planned to measure the cosmic microwave background (CMB) fluctuations with yet further accuracy, we may be able to piece together more clues about early Universe physics. In parallel with this observational effort, there has been tremendous progress in recent years in the construction of early Universe models in the framework of high energy physics and string theory.A particularly interesting class of models based on string theory is known as Dirac-Born-Infeld (DBI) inflation [1,2], associated with the motion of a D3-brane in a higherdimensional background spacetime. The characteristic of DBI inflation, and that which gives it its name, is that the action is of the Dirac-Born-Infeld type and thus contains nontrivial kinetic terms. Most studies of DBI inflation models (or even of string-based inflationary models) have so far concentrated on a single-field description meaning, in the DBI case, that the inflaton corresponds to a radial coordinate of the brane in the extra dimensions. Taking into account the ''angular'' coordinates of the brane naturally leads to a multifield description since each brane coordinate in the extra dimensions gives rise to a scalar field from the effective four-dimensional point of view. This setup has started to be explored only very recently [3,4].In this Letter, we show that the multifield DBI action contains some terms, higher order in spacetime gradients and vanishing in the homogeneous case, which have been overlooked. The inclusion of these terms leads to drastic consequences on the primordial fluctuations generated in these types of models. The scalar-type perturbations in multifield models can be divided into (instantaneous) adiabatic modes, fluctuations along the trajectory in field space, and entropy modes which are orthogonal to the former [5]. In contrast with previous expectations, we show that, in DBI models, these two classes of modes propagate with the same speed, namely, an effective speed of sound c s smaller than the speed of light. As a consequence, the amplification of quantum fluctuations occurs at the sound horizon crossing for both types of modes. Moreover, when c s 1, this leads to an enhancement of the amplitude of the entropy modes with respect to that of the usual adiabatic modes. As primordial non-Gaussianities -potentially detectable in forthcoming experiments if strong enough-discriminate between v...

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