We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at 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 also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis includes k -inflation, Dirac-Born-Infeld inflation and its multi-field extensions which have been recently studied. For this general class of models, we calculate the action to second order in the linear perturbations. We decompose the perturbations into an adiabatic mode, parallel to the background trajectory, and entropy modes. We show that all the entropy modes propagate with the speed of light whereas the adiabatic mode propagates with an effective speed of sound. We also identify the specific combination of entropy modes which sources the curvature perturbation on large scales. We then study in some detail the case of two scalar fields: we write explicitly the equations of motion for the adiabatic and entropy modes in a compact form and discuss their quantum fluctuations and primordial power spectra. *

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We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.Introduction.-Recent cosmic microwave background data from the Planck and BICEP2/Keck collaborations [1, 2] constrain the tensor-to-scalar ratio r < 0.12 (95% C.L.) and the spectral index of primordial density perturbations n s = 0.968 ± 0.006 (68% C.L.). The simplest slow-roll single-field inflationary models are in perfect agreement with these data and the lack of measurable primordial non-Gaussianities [3,4]. Amongst them, models coming with a concave plateau potential, such as Starobinsky inflation [5] and its numerous variants (see, e.g., [6-8]), are observationally favored. Despite this phenomenological success, embedding inflation into a realistic high-energy context remains a highly nontrivial task (see Refs. [9, 10] for reviews), as inflation is an ultraviolet-sensitive phenomenon. One manifestation of these difficulties is the so-called η problem, i.e., the fact that even Planck-suppressed corrections to an otherwise flat enough potential generically ruin inflation. Another challenge is the ubiquitous presence of extra scalar fields in models constructed in supergravity or string theory. In general, these fields participate in the inflationary dynamics and can substantially modify the corresponding observable predictions. In this respect, the simplest theoretical hope is to stabilize these extra scalars by providing them with a large mass, exceeding the value of the Hubble parameter H during inflation.In this Letter, we show the existence of a very general geometrical mechanism by which the noninflationary degrees of freedom can be destabilized during inflation, even if they have large masses in the static vacuum. This mechanism relies on the fact that generic multifield inflationary models are nonlinear sigma models, i.e., the kinetic part of their action reads L kin = − 1 2 G IJ (φ K )∂ µ φ I ∂ µ φ J , where the manifold described by the field space metric G IJ is generally curved. It is well known that the curvature of space manifests itself in the geodesic deviation:

Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space manifold overcoming the stabilizing force of the potential. This instability can drive the system away from its original path in field space into a new inflationary attractor, a scenario that we dub sidetracked inflation. We study this second phase and its observable consequences in several classes of two-field models. We show that cosmological fluctuations exhibit varied behaviours depending on the potential and the field space geometry, and that they can be captured by single-field effective theories with either a modified dispersion relation, a reduced speed of sound, or an imaginary one -the latter case describing a transient tachyonic growth of the fluctuations. We also numerically calculate the bispectrum with the transport approach, finding large non-Gaussianities of equilateral and orthogonal shapes. In the hyperbolic geometry the potentials of our models present a pole at the boundary of the Poincaré disk and we discuss their relationships with α-attractors.

We identify a characteristic pattern in the scalar-induced stochastic gravitational wave background from particle production during inflation. If particle production is sufficiently efficient, the scalar power spectrum exhibits O(1) oscillations periodic in k, characteristic of a sharp feature, with an exponentially enhanced envelope. We systematically study the properties of the induced spectrum of gravitational waves sourced after inflation and find that this inherits the periodic structure in k, resulting in a peak in the gravitational wave energy density spectrum with O(10%) modulations. The frequency of the oscillation in the scalar power spectrum is determined by the scale of the feature during inflation and in turn sets the frequency of modulations in the gravitational wave signal. We present an explicit realisation of this phenomenon in the framework of multifield inflation, in the form of a strong sharp turn in the inflationary trajectory. The resulting stochastic background is potentially detectable in future gravitational wave observatories, and considerations of backreaction and perturbativity can be used to constrain the parameter space from the theoretical side. Our work motivates more extensive research linking primordial features to observable properties of the stochastic background of gravitational waves, and dedicated development in data analysis for their detection.

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We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-singlefield inflation, with scalar masses of order H, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.