Attractors, bifurcations and curvature in multi-field inflation

Abstract

Recent years have seen the introduction of various multi-field inflationary scenarios in which the curvature and geodesics of the scalar manifold play a crucial role. We outline a simple description that unifies these different proposals and discuss their stability criteria. We demonstrate how the underlying dynamics is governed by an effective potential, whose critical points and bifurcations determine the late-time behaviour of the system, thus unifying hyperinflation, angular, orbital and side-tracked inflation. Interestingly, we show that hyperinflation is a special case of side-tracked inflation, relying on the enhanced isometries of the hyperbolic manifold. We provide the explicit coordinate transformation that maps the two models into each other. Finally, we relax the assumption of a field-space isometry along the inflationary direction that has been considered a prerequisite in the literature so far. We explicitly construct inflationary solutions that do not proceed along a field-space isometry or geodesic and use them to discuss stability criteria.

Dynamics of Einstein–Aether scalar field cosmology

“…Moreover, we study the cosmological asymptotic solutions provided by this model by determining the stationary points of the field equations [51][52][53]. Such analysis is essential in order to infer about the viability of the model [54].…”

The multi-field, rapid-turn inflationary solution

“…Hyperinflation [9,10,38] is a rapidly turning solution possible whenever the field space is hyperbolic, and the potential sufficiently steep around the origin. As previously noted by [23], it is a special case of sidetracked inflation [13,14].…”

“…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].…”

Integrable cosmological models with an additional scalar field

“…After the metric transformation, one obtains models with a nonstandard kinetic part, so-called chiral cosmological models [38][39][40][41][42][43]. Mathematical properties of such models attract a lot of attention [38,40,[44][45][46][47][48][49][50][51][52][53][54].…”