Inflationary attractors in metric-affine gravity
Abstract
We study single-field slow-roll inflation in metric-affine gravity (MAG). We consider the most general action up to operators linear in curvature and quadratic in the distortion, without propagating torsion and non-metricity. We first impose projective invariance and promote every coefficient to a function of the scalar field. After integrating out the non-dynamical distortion, the net contribution is a correction k(ϕ) to the scalar kinetic term. We then consider the class of ξ-attractors for which the non-minimal couplings and the scalar potential are fixed by a single function f(ϕ). It is well-known that in the metric formulation the strong-coupling regime is universally the Starobinsky attractor. In the Palatini framework, instead, this attractor is lost and the predictions become model-dependent. Here, we show that the MAG framework restores universality: in the strong coupling limit with finite ratios of the distortion couplings to ξ we have an α-attractor, ns=1−2/N* and r=12α/N*2, with α=1+ζ/(6ξ). The ratio ζ/ξ encodes the distortion contribution. Starobinsky and Palatini inflation are recovered as specific limits. Through a numerical parameter scan we show that almost all the healthy points lie on one of the two attractors : either Nieh-Yan-like inflation (studied in a previous work and extended here) or the new MAG α-attractor found here. Finally, we explicitly drop projective invariance and analyse the general MAG theory. The same large-field asymptotic structure survives. We conclude that no extra inflationary phenomenology is reached by the non-projectively invariant operators: the α-attractor is a general prediction of MAG.
Related
- Palatini inflationary (non-)attractors: Universal mapping of observables
- Inflationary models in a minimally coupled f(R,T) gravity: Constraints from Planck, BICEP/Keck, and ACT
- Natural Metric-Affine Inflation: Reloaded
- The metric-affine mathringR2 scalaron: parameter-free inflation
- Interacting fluid cosmologies from the metric-affine framework
BibTeX
@misc{andrei2026inflationary,
title = {{Inflationary attractors in metric-affine gravity}},
author = {Ilaria Andrei and Christian Dioguardi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06750},
eprint = {2611.06750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06750},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inflationary attractors in metric-affine gravity
AU - Ilaria Andrei
AU - Christian Dioguardi
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06750
UR - https://arxiv.org/abs/2611.06750
AB - We study single-field slow-roll inflation in metric-affine gravity (MAG). We consider the most general action up to operators linear in curvature and quadratic in the distortion, without propagating torsion and non-metricity. We first impose projective invariance and promote every coefficient to a function of the scalar field. After integrating out the non-dynamical distortion, the net contribution is a correction k(ϕ) to the scalar kinetic term. We then consider the class of ξ-attractors for which the non-minimal couplings and the scalar potential are fixed by a single function f(ϕ). It is well-known that in the metric formulation the strong-coupling regime is universally the Starobinsky attractor. In the Palatini framework, instead, this attractor is lost and the predictions become model-dependent. Here, we show that the MAG framework restores universality: in the strong coupling limit with finite ratios of the distortion couplings to ξ we have an α-attractor, n_s=1−2/N_* and r=12α/N_*^2, with α=1+ζ/(6ξ). The ratio ζ/ξ encodes the distortion contribution. Starobinsky and Palatini inflation are recovered as specific limits. Through a numerical parameter scan we show that almost all the healthy points lie on one of the two attractors : either Nieh-Yan-like inflation (studied in a previous work and extended here) or the new MAG α-attractor found here. Finally, we explicitly drop projective invariance and analyse the general MAG theory. The same large-field asymptotic structure survives. We conclude that no extra inflationary phenomenology is reached by the non-projectively invariant operators: the α-attractor is a general prediction of MAG.
ER -