Waterfall-modulated α-attractors
Abstract
Hybrid α-attractor models \cite{Kallosh:2022ggf} can have significantly greater values of ns and smaller r, while preserving the relation r≅ 3α(1−ns)2, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field α-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point φc. This allows one to increase the effective number of e-foldings Nc in formulas like ns≃ 1−2over Nc, r≃ 12 αover Nc2. By changing the waterfall's steepness and location, one can continuously move the predictions along the curves with r≅ 3α(1−ns)2 as ns increases and r decreases. We also study the effect of waterfall insertions and uplift on ns in quintessential α-attractors that describe inflation and dynamical dark energy.
Related
- Pseudo-Nambu-Goldstone inflation with ZN symmetric waterfall fields
- Unification of polynomial and exponential cosmological attractors
- Palatini inflationary (non-)attractors: Universal mapping of observables
- Spiralling into Dark Energy: Axio-Dilaton Attractors in Light of Current Data
- Cosmological evolution and late-time attractors in axion-monopole interacting dark energy
BibTeX
@misc{kallosh2026waterfallmodulated,
title = {{Waterfall-modulated $α$-attractors}},
author = {Renata Kallosh and Andrei Linde and Yusuke Yamada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.12819},
eprint = {2608.12819},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.12819},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Waterfall-modulated α-attractors
AU - Renata Kallosh
AU - Andrei Linde
AU - Yusuke Yamada
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.12819
UR - https://arxiv.org/abs/2608.12819
AB - Hybrid α-attractor models \cite{Kallosh:2022ggf} can have significantly greater values of n_s and smaller r, while preserving the relation r≅ 3α(1−n_s)^2, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field α-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point φ_c. This allows one to increase the effective number of e-foldings N_c in formulas like n_s≃ 1−2over N_c, r≃ 12 αover N_c^2. By changing the waterfall's steepness and location, one can continuously move the predictions along the curves with r≅ 3α(1−n_s)^2 as n_s increases and r decreases. We also study the effect of waterfall insertions and uplift on n_s in quintessential α-attractors that describe inflation and dynamical dark energy.
ER -