We study cosmological perturbations in two-field inflation, allowing for non-standard kinetic terms. We calculate analytically the spectra of curvature and isocurvature modes at Hubble crossing, up to first order in the slow-roll parameters. We also compute numerically the evolution of the curvature and isocurvature modes from well within the Hubble radius until the end of inflation. We show explicitly for a few examples, including the recently proposed model of ‘roulette’ inflation, how isocurvature perturbations affect significantly the curvature perturbation between Hubble crossing and the end of inflation.

We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description.However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory.In particular, the predictions of the model are sensitive to the relative hierarchy between the coupling and the mass of the heavy mode. As a result, observables are not given unambiguously in terms of the parameters of an effectively single field model with non-trivial sound speed. Finally, the requirement that the sound horizon crossing occurs within the regime of validity of the effective theory leads to a lower bound on the sound speed. Our analysis is done in an extremely simple toy model of slow-roll inflation, which is chosen for its tractability, but is non-trivial enough to illustrate the richness of the dynamics in non-canonical multi-field models.

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:

In cascade inflation and some other string inflation models, collisions of mobile branes with other branes or orbifold planes occur and lead to interesting cosmological signatures. The fundamental M/string-theory description of these collisions is still lacking but it is clear that the inflaton looses part of its energy to some form of brane matter, e.g. a component of tensionless strings. In the absence of a fundamental description, we assume a general barotropic fluid on the brane, which absorbs part of the inflaton's energy. The fluid is modeled by a scalar with a suitable exponential potential to arrive at a full-fledged field theory model. We study numerically the impact of the energy transfer from the inflaton to the scalar on curvature and isocurvature perturbations and demonstrate explicitly that the curvature power spectrum gets modulated by oscillations which damp away toward smaller scales. Even though, the contribution of isocurvature perturbations decays toward the end of inflation, they induce curvature perturbations on scales that exit the horizon before the collision. We consider cases where the scalar behaves like radiation, matter or a web of cosmic strings and discuss the differences in the resulting power spectra.