# A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians

**Authors:** Christine C. Dantas  
**arXiv:** [2605.13921](https://arxiv.org/abs/2605.13921)  
**Date:** 2026-05-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2605.13921v1/

## Key points

- Christine C. Dantas explores limitations of geometrizing non-quadratic cosmological dynamics using the Eisenhart-Duval lift (ED) framework
- The ED lift embeds classical trajectories into null geodesics of a higher-dimensional Lorentzian spacetime and requires a natural Hamiltonian that is quadratic in canonical momenta
- Mini-superspace cosmological models with non-natural Hamiltonians, like those in Loop Quantum Cosmology, do not fit within the metric framework of the ED lift
- Non-polynomial Hamiltonians lead to a kinematical no-go theorem, indicating that non-quadratic cosmological dynamics cannot be effectively geometrized through ED constructions
- Quantum-corrected bounce models illustrate the structural limitation of metric geometrization within the ED framework
- Dantas' findings highlight challenges in applying the ED lift to quantum cosmologies with non-traditional Hamiltonians and stress the importance of considering the nature of the Hamiltonian in geometric constructions

## Summary

In her paper titled "A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians," Christine C. Dantas explores the limitations of geometrizing non-quadratic cosmological dynamics using the Eisenhart-Duval lift (ED) framework. The ED lift is a method that embeds classical trajectories into null geodesics of a higher-dimensional Lorentzian spacetime and requires a natural Hamiltonian that is quadratic in canonical momenta. Dantas highlights that mini-superspace cosmological models governed by non-natural Hamiltonians, such as those found in Loop Quantum Cosmology with polymer-modified Hamiltonians, do not fit within the metric framework of the ED lift. These non-polynomial Hamiltonians lead to a kinematical no-go theorem, indicating that non-quadratic cosmological dynamics cannot be effectively geometrized through ED constructions. By examining quantum-corrected bounce models as an example, Dantas illustrates the structural limitation of metric geometrization within the ED framework. Her findings shed light on the challenges faced when attempting to apply the ED lift to quantum cosmologies with non-traditional Hamiltonians and emphasize the importance of considering the nature of the Hamiltonian in geometric constructions of dynamical systems.