Geometrical Destabilization of Inflation

Abstract

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:

On the inflationary massive field with a curved field manifold

“…But as discussed above (and also pointed out in Ref. [20,36,74] previously), this operator may give nontrivial corrections to the isocurvature mass. One can interpret this effect by the right diagram in Fig.…”

Quantum diffusion during inflation and primordial black holes

“…In this model, inflation does not end by slow-roll violation but another mechanism must be invoked [67][68][69][70][71]. We also assume that the potential is in the vacuum-dominated regime for the range of field values relevant for PBH formation, so that φ φ 0 .…”

Further Refining the de Sitter Swampland Conjecture

“…The matrix is the mass (square) matrix for constant fields or constant fluctuations; see e.g. [] for the non‐constant case. The eigenvalues of this matrix then give the mass spectrum, and whether their minimum is negative tells us if a tachyon is present.…”