Multi-field inflation in high-slope potentials

Abstract

Inspired by the swampland distance conjecture and the high-slope conjecture, we present two families of multi-field inflationary potentials compatible with the conjectures along the trajectory. One family is a helix-type potential that satisfies the conjectures only locally. This family inflates with V H and produces Planck-compatible scalar perturbations, but a too-high tensor power. Our other family of potentials globally satisfies the swampland conjectures and is in negatively-curved field space. It balances the potential gradient against the geometry to generate high turning rates. Due to the form of the potential, this model has exactly massless entropic perturbations and a light adiabatic mode. In the superhorizon limit, the entropic mode freezes out, which sources linear growth of the adiabatic mode. In contrast to hyperinflation, both families remain under perturbative control.

The multi-field, rapid-turn inflationary solution

“…This growth must be considered in any phenomenological study of rapid-turn trajectories. We end by noting that phenomenologically viable rapid-turn trajectories have been found in [11,14,28], in which the mass scale of inflation is lowered to ensure an adiabatic power spectrum that is consistent with observations.…”

“…Rapidly turning trajectories in multi-dimensional field spaces have been of much recent interest: they can yield inflation and quintessence in potentials satisfying the de-Sitter conjecture [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and they can form primordial black holes [18][19][20][21]. Rapidly turning inflation models are also profound in their own right, as they can exhibit dynamics very different from single-field inflation while being phenomenologically viable [14,15,[22][23][24][25][26][27][28].…”

Fat inflatons, large turns and the η-problem

“…In the APR model inflation does not end, so the values of the parameters are given at the start of inflation. In this example, Ω decreases, while Ω/H remains almost constant (see [58] Table 6. Ratio of masses to the Hubble parameter for the fat inflationary models as indicated.…”

“…As fat inflation models with large turning rates, we show an example of two-field natural inflation model discussed in [34] (AAW1), the recent three field model in [58] (APR) and the sidetrack models in [24]. These all have large Ω/H, and only the sidetrack models have a non-zero negative curvature R. In table 6 we show the ratio between the masses and the Hubble parameter for AW1, APR and the sidetrack models (both the minimal an hyperbolic examples have similar mass hierarchies).…”

“…In appendix A we collected examples of field theory multifield models in the literature, which happen to belong to the fat slow-roll attractor. These include a recently discussed three field model in [58] (APR) where the lightest field is sixty times the Hubble scale, m 1 /H 60, while the heaviest is thousand times heavier m 3 /H 4500. The sidetrack models, where there is a transition from a standard slow-roll trajectory with a light and a heavy field, to a fat slow-roll trajectory, with both scalar fields having larger masses than the Hubble scale.…”