The multi-field, rapid-turn inflationary solution

Abstract

There are well-known criteria on the potential and field-space geometry for determining if slow-roll, slow-turn, multi-field inflation is possible. However, even though it has been a topic of much recent interest, slow-roll, rapid-turn inflation only has such criteria in the restriction to two fields. In this work, we generalize the two-field, rapid-turn inflationary attractor to an arbitrary number of fields. We quantify a limit, which we dub extreme turning, in which rapid-turn solutions may be found efficiently and develop methods to do so. In particular, simple results arise when the covariant Hessian of the potential has an eigenvector in close alignment with the gradient — a situation we find to be common and we prove generic in two-field hyperbolic geometries. We verify our methods on several known rapid-turn models and search two type-IIA constructions for rapid-turn trajectories. For the first time, we are able to efficiently search for these solutions and even exclude slow-roll, rapid-turn inflation from one potential.

Tachyonic de Sitter Solutions of 10d Type II Supergravities

“…We note though that most de Sitter solutions found have an close to −1, remaining consistent with the refined de Sitter conjecture of [83,84], while having possible interest for multi‐field inflation or quintessence models of the kind [ 106–110 ] and more recently. [ 111–114 ] The validity of these 10d supergravity de Sitter solutions as classical perturbative string backgrounds remains to be checked following, [ 75 ] while we recall that no example of such a de Sitter background is known up‐to‐date.…”

Inflation with strongly non-geodesic motion: theoretical motivations and observational imprints

“…Actually, one can show kinematically that one can inflate on Planck-steep potentials only at the condition that the motion is strongly non-geodesic [10]. The fact that this can naturally arise dynamically in a negatively curved field space is particularly interesting, and the study of such kind of attractors has been pursued actively in recent years (see for instance [4,6,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]). However, as already anticipated in [6], it is important to stress that inflation with strongly non-geodesic motion does not alleviate the difficulties to embed inflation in high-energy physics, which simply manifest themselves in a different manner than in slow-roll.…”

Anisotropic Spacetimes in Chiral Scalar Field Cosmology

“…The kinetic energy of the two scalar field lies on a two-dimensional maximally symmetric space of negative curvature, hyperbolic space. This multi-scalar field model provides the so-called hyperbolic inflation [23,25]. However, there are various applications of this model and in other areas of the cosmic evolution [26][27][28][29][30][31][32][33][34][35].…”