UV completion pathways for torsion and non-metricity inflation

Ascertain ultraviolet completions for torsion-based (f(T), Einstein–Cartan) and non-metricity-based (f(Q)) inflationary theories by establishing consistent embeddings within string theory, supergravity, or asymptotically safe quantum gravity, and delineate the conditions under which these embeddings reproduce viable inflationary phenomenology.

Background

Unlike curvature-based Starobinsky inflation, torsion and non-metricity frameworks lack widely accepted UV completions. The review highlights the importance of connecting these geometric models to fundamental theories to ensure quantum consistency and predictivity.

Clarifying UV embeddings would also address issues such as unitarity, strong coupling, and the validity of effective field theory during inflation.

References

We highlight several key open problems: What are the ultraviolet completions for torsion-based (f(T), Einstein–Cartan) and non-metricity-based (f(Q)) inflationary theories? Can these theories be embedded consistently in a string-theoretic, supergravity, or asymptotically safe quantum gravity framework?

— From geometry to cosmology: a pedagogical review of inflation in curvature, torsion, and extended gravity theories  (2509.14306 - Momeni, 17 Sep 2025) in Section: Open Questions and Future Directions

Although a complete theory of quantum gravity has not yet been established, we consider the possibility that its classical limit may admit an Einstein-Cartan description before general relativity is recovered in the torsion-free limit.

— Holographic dark energy in Einstein-Cartan spin cosmology  (2609.36853 - Yun et al., 29 Sep 2026) in Figure 1 caption, Section I, Introduction