On backreaction effects in geometrical destabilisation of inflation

Abstract

We study the geometrical instability arising in multi-field models of inflation with negatively-curved field space. We analyse how the homogeneous background evolves in presence of geometrical destabilisation, and show that, in simple models, a kinematical backreaction effect takes place that shuts off the instability. We also follow the evolution of the unstable scalar fluctuations and show that, in most situations, they must remain in the perturbative regime in order to satisfy observational constraints. We conclude that, in the simplest models of geometrical destabilisation, inflation does not end prematurely, but rather proceeds along a modified, sidetracked, field-space trajectory.is a holomorphic function of the fields φ i . Upon expressing the Lagrangian (2.2) in terms of real scalar fields, it is indeed of the type (2.1), though with a specific structure dictated by the superpotential and the Kähler potential of the theory. Note that in this context, the description of inflation using multiple fields is a built-in feature, as even the simplest models involve one complex scalar field, i.e. two real scalar fields. We also stress that the fact that the Kähler metric generically describes a curved internal space is dictated by the theoretical structure of these theories. For instance, in the case of a string compactification with N = 1 supersymmetry, K and W are related to geometric properties of the compactification.

Hyper-Non-Gaussianities in Inflation with Strongly Nongeodesic Motion

“…Fig. 5 is the full plot of the reduced bispectrum derived from the EFT, using the value x = 10 and A = −0.33 as in (16). Although we have used a single one-dimensional slice of f N L for the estimation of x and A, one can see an overall excellent agreement for the global shape of the bispectrum between the analytical and numerical results (see Fig.…”

“…This in turn relaxes the conditions of slow-roll to allow for potentials that are steep in Planck units [8,9], a welcome feature in view of the eta problem and the recently much discussed swampland conjectures [10,11]. Lastly, internal field spaces with negative curvature are at the origin of the phenomenon of geometrical destabilization [12][13][14][15][16], in which non-inflationary degrees of freedom, even heavy ones, can dramatically affect the fate of inflation.A concrete scenario in which the consequences of a hyperbolic field space have been studied is the proposal of "hyperinflation" [17], that has recently been under scrutiny [18,19]. The intuitive picture of this set-up is that of an inflationary trajectory corresponding to a circular motion around the minimum of a (circularly symmetric) scalar potential.…”

“…This in turn relaxes the conditions of slow-roll to allow for potentials that are steep in Planck units [8,9], a welcome feature in view of the eta problem and the recently much discussed swampland conjectures [10,11]. Lastly, internal field spaces with negative curvature are at the origin of the phenomenon of geometrical destabilization [12][13][14][15][16], in which non-inflationary degrees of freedom, even heavy ones, can dramatically affect the fate of inflation.…”

Scaling attractors in multi-field inflation

“…This is reminiscent of the effects of geometric destabilization giving rise to sidetracked inflation. A minor difference is found in the fact that is constant for scaling solutions, and thus it cannot trigger geometrical destabilization, as it does in realistic inflationary set-ups [7,42]. Furthermore, our analysis does not take into account quantum fluctuations, which in some cases are crucial in destabilizing a system, that could classically be made to lie arbitrarily (exponentially) close to an unstable trajectory.…”

On the F-term problem and quintessence supersymmetry breaking

“…We also see why such mechanism (which is intrinsic in supergravity embeddings) may instead pose a catastrophic threat to otherwise healthy quintessence models, depending on the kinetic mixings. This effect is already studied within the context of inflationary cosmology, because it can ruin inflation, and therefore is dubbed "geometrical destabilization" [16][17][18][19]. In the fourth section we turn to the gaugini masses which are of course also influenced by the F-term problem.…”